PRACTICAL  PYEOMETEY 


THE   THEORY,    CALIBRATION   AND   USE   OF   IN- 
STRUMENTS FOR  THE   MEASUREMENT 
OF  HIGH  TEMPERATURES 


BY 

ERVIN  S.  FERRY 
GLENN  A.  SHOOK  JACOB  R.  COLLINS 


FIRST   EDITION 


NEW  YORK 
JOHN  WILEY  &  SONS,  INC. 

LONDON:   CHAPMAN   &   HALL,  LIMITED 

1917 


COPYRIGHT,  1917, 

BY 
ERVIN  S.  FERRY 


Stanhope 

F.    H.  GILSON  COMPANT 

BOSTON,  U.S.A. 


PREFACE 


THE  day  is  already  past  when  f  oundrymen  and  steel  workers  de- 
pend upon  the  eye  to  judge  the  temperatures  of  their  product  in 
the  various  stages  of  its  heat  treatment,  when  makers  of  ceramic 
products  depend  upon  the  indication  of  fusible  cones,  and  when 
operators  of  cold  storage  plants  are  content  to  observe  numerous 
thermometers  scattered  throughout  their  establishments.  The 
requirements  of  modern  industrial  processes  and  the  severe  com- 
petition of  commercial  enterprises  now  require  not  only  more 
precise  knowledge  of  temperatures,  but  hi  many  cases  also  re- 
quire a  continuous  automatic  record  of  the  temperature  state 
extending  over  an  interval  of  time. 

Several  years  ago,  anticipating  the  need  by  technical  students 
of  a  Course  in  High  Temperature  Measurements,  the  work  of 
testing  the  various  methods  and  apparatus  was  begun.  After 
three  years  devoted  to  this  survey,  a  course  was  organized  and 
offered.  It  was  received  with  such  favor  that  it  was  made  a 
required  subject  in  the  plan  of  study  for  students  of  chemical 
engineering  at  Purdue  University.  Each  year  since  then,  a  new 
edition  of  Notes,  in  mimeographed  form,  has  been  put  into  the 
hands  of  the  students.  It  has  now  been  thought  proper  to  put  into 
more  readable  and  permanent  form  the  results  of  this  experience. 

In  the  present  book,  the  needs  of  three  distinct  classes  of  readers 
have  been  kept  in  mind  —  college  students,  technically  trained 
men  who  deal  with  processes  requiring  high  temperature  meas- 
urements, and  less  trained  observers  who  may  make  the  meas- 
urements. For  the  first  two  classes,  who  require  much  fuller 
theoretical  discussions  than  the  latter,  are  developed  in  some 
detail  the  principles  involved.  In  some  cases  the  discussion  of 
these  principles  involve  physical  and  mathematical  ideas  beyond 
the  training  of  the  average  observer.  For  the  less  trained  observer 


O  *t  O  O  A 


iv  PREFACE 

are  given  the  physical  principles  and  manipulative  details  with 
which  he  would  require  familiarity,  many  of  which  would  have 
been  omitted  if  the  needs  of  only  the  more  trained  readers  had 
been  kept  in  mind. 

At  all  times  the  publications,  experience  and  advice  of  G.  K. 
Burgess  and  the  other  members  of  the  staff  of  the  Bureau  of  Stand- 
ards have  been  generously  extended  to  us  and  freely  used.  We 
are  glad  to  take  the  opportunity  to  thank  them  for  their  many 
courtesies. 

All  of  the  illustrations  have  been  engraved  especially  for  this 
book,  but  some  of  them  are  copies  of  catalogue  plates  of  standard 
commercial  apparatus. 

E.  S.  F. 
G.  A.  S. 
J.  R.  C. 

PHYSICS  LABORATORY,  PURDUE  UNIVERSITY, 
LAFAYETTE,  IND. 


CONTENTS 


CHAPTER  I 

STANDARD   TEMPERATURE   SCALES 

ART.  PAGE 

1.  The  Comparison  of  Temperatures 1 

2.  Scales  of  Temperature 2 

3.  The  Centigrade  and  Fahrenheit  Degrees 3 

4.  The  Thermodynamic  Temperature  Scale 4 

5.  The  Ideal  Gas  Temperature  Scale 5 

6.  The  Normal  Thermometer 6 

7.  The  Black-body  Temperature  Scale 8 

8.  The  Application  of  the  Three  Standard  Temperature  Scales 10 


CHAPTER  II 
RESISTANCE  PYROMETRY 

9.   Relation  between  Resistance  and  Temperature 12 

10.  The  Wheatstone  Bridge 12 

11.  Direct  Reading  Resistance  Pyrometers 14 

12.  The  Availability  of  Resistance  Pyrometers  to  Industrial  Use 15 

13.  Recording  Resistance  Pyrometers 16 

Exp.  1.   Calibration  of  a  Resistance  Pyrometer 20 

CHAPTER  III 
THERMOELECTRIC  PYROMETRY 

The  Seebeck  Effect 24 

Application  to  Temperature  Measurement 25 

Choice  of  Metals  for  Thermoelectric  Couples 26 

The  Construction  of  Thermoelectric  Pyrometers 28 

Indicators  for  Thermoelectric  Pyrometers 29 

Millivoltmeter  Indicators 29 

The  Potentiometer  Method  of  Measuring  Electromotive  Forces 31 

Potentiometer  Indicators  for  Thermoelectric  Pyrometers 34 

The  Deflection  Potentiometer 35 

Recording  Thermoelectric  Pyrometers 39 

v 


vi  CONTENTS 

ART.  PAGE 

24.  The  Cold-Junction  Correction 40 

25.  Cold- Junction  Correction  when  the  Temperature   of  the   Cold- 

Junction  is  not  Constant 49 

26.  Shop  Methods  for  Reducing  the  Errors  Due  to  Variation  in  the 

Temperature  of  the  Cold  Junction 51 

27.  Advantages  and  Disadvantages  of  the  Thermoelectric  Method  of 

Measuring  Temperatures 55 

28.  The  Installation  of  Thermoelectric  Pyrometers 56 

Exp.  2.   Calibration  of  a  Thermoelectric  Couple 58 

Exp.  3.    The  Construction  and  Test  of  Thermoelectric  Couples 62 

Exp.  4.    Determination  of   Temperatures  by  Means  of  a   Thermo- 
electric Pyrometer  with  the  Cold  Junction  not  Maintained 

at  a  Constant  Temperature 66 

Exp.  5.   Determination  of  the  Transformation  Points  of  a  Specimen 

of  Steel 67 


CHAPTER  IV 
RADIATION  PYROMETRY 

29.  The  Experimental  Realization  of  Black-Body  Radiation 71 

30.  The  General  Principles  of  Radiation  Pyrometry 73 

31.  The  Fe*ry  Thermoelectric  Mirror  Radiation  Pyrometer 75 

32.  The  Relation  between  the  Energy  Rate  at  a  Point  and  the  Distance 

from  the  Source 79 

33.  The  F&y  Spiral  Pyrometer 79 

34.  Fixed  Focus  Radiation  Pyrometers 80 

35.  The  Foster  and  the  Brown  Fixed  Focus  Pyrometers 81 

36.  Thwing's  Fixed  Focus  Radiation  Pyrometer 82 

37.  Radiation  Pyrometers  Indicate  Black-Body  Temperatures 83 

38.  Precautions  in  using  Radiation  Pyrometers 84 

Exp.  6.   Calibration  of  a  Radiation  Pyrometer 85 

CHAPTER  V 
OPTICAL  PYROMETRY 

39.  Kirchhoff's  Law 89 

40.  Wien's  Distribution  Law 90 

41.  The  Thermodynamic  Temperature  Corresponding  to  a  given  Black- 

Body  Temperature 91 

42.  The  Equality  of  Brightness  Method  of  Measuring  Temperature ...  94 

43.  The  General  Optical  Pyrometer  Equation 97 

44.  The  Color  Identity  Method  of  Measuring  Temperature 100 

45.  Le  Chatelier's  Optical  Pyrometer 100 


CONTENTS  vii 

ART.  PAGE 

46.  The  F4ry  Absorption  Pyrometer 102 

47.  The  Shore  Pyroscope 103 

48.  The  Holborn-Kurlbaum  Optical  Pyrometer 104 

49.  The  Wanner  Optical  Pyrometer 105 

50.  The  Wide  Filament  Pyrometer  Comparison  Lamp 107 

Exp.    7.   Calibration  of  a  Le  Chatelier  Optical  Pyrometer 108 

Exp.    8.    Calibration  of  a  Wanner  Optical  Pyrometer 114 

Exp.    9.   Calibration  of  a  Holborn-Kurlbaum  Optical  Pyrometer. .  . .  122 
Exp.  10.    Determination  of  the  Melting  Point  of  a  Very  Small  Speci- 
men of  a  Substance 126 

Exp.  11.    The  Determination  of  the  Relation  between  the  Luminous 
Intensity  and  the  Temperature  of  an  Incandescent  Lamp 

Filament 127 

Exp.  12.   Calibration  of  a  Fery  Absorption  Pyrometer 131 

Exp.  13.   Calibration  of  a  Color  Identity  Optical  Pyrometer 133 

Exp.  14.    The  Measurement  of  Actual  Temperatures  of  a  Gray  Body  135 


CONCLUSION 

51.  The  Selection  of  Pyrometers  for  Particular  Purposes 138 

TABLES 

1.  Boiling  Point  of  Water  under  Different  Barometric  Pressures 141 

2.  Corrections  for  the  Influence  of  Gravity  in  the  Height  of  a  Barometer  142 

3.  Values  of  log  (tan20)  for  Use  with  the  Wanner  Optical  Pyrometer.  .  143 


PRACTICAL    PYROMETRY 

CHAPTER  I 
STANDARD  TEMPERATURE   SCALES 

1.  The  Comparison  of  Temperatures.  —  Lengths  can  be 
directly  measured  by  means  of  a  foot  rule,  a  meter  bar,  a  survey- 
or's chain  or  other  standard  of  length.  Similarly,  volumes  can  be 
measured  in  terms  of  some  standard  of  volume  such  as  a  gallon, 
bushel,  or  cubic  foot.  Temperatures,  however,  cannot  be  di- 
rectly measured.  In  fact,  temperatures  can  be  compared  only 
indirectly  in  terms  of  some  property  which  changes  in  magnitude 
when  temperature  changes.  For  example,  since  when  under 
constant  pressure  the  length  and  volume  of  most  substances 
increase  as  their  temperature  increases,  changes  of  length  and 
volume  can  be  used  for  the  comparison  of  temperatures. 

Again,  since  the  pressure  of  a  fixed  mass  of  gas  kept  at  con- 
stant volume  increases  when  the  temperature  of  the  gas  is  raised, 
changes  in  the  pressure  of  a  gas  under  these  conditions  can  be 
used  as  a  measure  of  the  changes  of  temperature. 

If  a  circuit  be  formed  of  wires  of  two  different  metals,  and 
if  the  two  junctions  of  the  metals  be  kept  at  different  temperatures, 
electromotive  forces  of  different  values  are  usually  developed  at 
the  two  junctions  and  in  the  wires  between  the  junctions.  For 
wires  of  given  materials,  the  resultant  electromotive  force  is  a 
function  of  the  difference  of  temperature  of  the  two  junctions. 
Since  electromotive  forces  are  readily  measured,  this  thermo- 
electric effect  can  be  used  for  the  comparison  of  temperature 
differences. 

Again,  since  the  total  energy  radiated  per  second  by  a  hot 

1 


2  STANDARD  TEMPERATURE  SCALES 

body  increases  when  tiie  temperature  is  increased,  we  might 
measure  temperature  in  terms  of  the  rate  of  radiation  of  energy 
from  unit  surface  of  a  body. 

In  fact,  each  of  the  properties  mentioned  is  employed  in  the 
comparison  of  temperatures.  For  one  set  of  conditions  a  device 
based  upon  one  of  these  properties  is  best  suited,  while  under 
other  conditions  a  device  based  upon  a  different  property  is 
preferable. 

2.  Scales  of  Temperature.  —  For  the  specification  of  a  tem- 
perature we  require  not  only  a  means  of  showing  which  of  two 
bodies  is  at  the  higher  temperature,  but  also  a  scheme  for  indi- 
cating numerically  the  amount  that  the  temperature  of  one  body 
exceeds  that  of  the  other.  That  is,  we  must  have  a  scale  of 
temperature. 

Any  one  of  the  properties  of  matter  previously  mentioned  can 
be  used  as  a  basis  for  the  construction  of  a  temperature  scale. 
For  instance,  if  at  a  certain  temperature  the  length  of  a  given 
copper  rod  is  midway  between  the  length  of  the  same  rod  when  at 
the  temperature  of  melting  ice  and  that  of  the  steam  from  boiling 
water,  we  might  say  that  the  certain  temperature  is  midway 
between  the  temperature  of  the  melting  ice  and  that  of  the  steam 
from  boiling  water.  Then,  if  the  temperature  of  melting  ice  be 
denoted  by  zero,  and  the  temperature  of  steam  from  boiling  water 
by  100,  the  certain  temperature  would  be  50.  We  might  go  fur- 
ther and  call  those  temperature  differences  equal  that  produce 
equal  differences  in  the  length  of  a  copper  rod.  We  would  then 
have  a  temperature  scale  based  on  the  expansion  of  copper. 

Similarly,  if  we  were  to  call  those  temperature  changes  equal 
which  produce  equal  changes  in  the  pressure  of  a  fixed  mass  of 
a  certain  gas  kept  at  constant  volume,  we  would  have  a  tempera- 
ture scale  based  on  a  different  property  of  matter. 

In  the  same  manner,  by  calling  those  differences  of  temperature 
equal  that  produce  equal  differences  in  the  resistance  of  a  wire 
made  of  given  material,  we  could  construct  a  different  tempera- 
ture scale. 

But  if  we  define  equal  increments  of  temperature  in  terms  of 


THE  CENTIGRADE  AND  THE  FAHRENHEIT  DEGREES   3 

equal  increments  of  length  of  a  copper  rod,  we  are  no  longer 
at  liberty  to  call  those  increments  of  temperature  equal  which 
produce  equal  increments  of  the  pressure  of  a  fixed  mass  of  gas 
kept  at  constant  volume;  nor  those  increments  of  temperature 
which  produce  equal  increments  of  electric  resistance;  nor  those 
increments  of  temperature  which  produce  equal  increments  of 
any  other  property  of  matter.  Indeed,  we  find  that  any  one 
of  the  methods  of  defining  equal  increments  of  temperature 
leads  to  increments  of  temperature  which  would  not  be  equal 
if  any  of  the  other  methods  of  definition  had  been  adopted. 

3.  The  Centigrade  and  the  Fahrenheit  Degrees.  —  In  the 
construction  of  any  temperature  scale,  two  definite  temperatures 
are  required,  and  definite  numerical  values  must  be  assigned  to 
those  temperatures.  The  particular  temperatures  selected,  as 
well  as  the  particular  numbers  employed  to  designate  these 
temperatures,  are  matters  of  arbitrary  convention.  But  in  order 
that  readings  made  from  different  thermometers  may  be  com- 
parable, physicists  have  agreed  upon  two  particular  tempera- 
tures for  the  two  fixed  points.  For  one  is  taken  the  temperature 
of  melting  ice,  and  for  the  other,  the  temperature  of  the  steam 
from  boiling  water  —  both  under  a  barometric  pressure  of  76 
centimeters  of  mercury. 

Celsius  assigned  the  number  0  to  the  temperature  of  melting 
ice,  and  100  to  the  temperature  of  steam  rising  from  boiling 
water.  As  there  are  100  degrees  between  the  two  fixed  points, 
this  scale  is  usually  called  the  centigrade  scale.  One  centigrade 
degree  is  one  hundreth  of  the  temperature  interval  between  the 
temperature  of  melting  ice  and  the  temperature  of  steam  rising 
from  boiling  water. 

Fahrenheit  assigned  the  number  32  to  the  temperature  of 
melting  ice,  and  212  to  the  temperature  of  steam  rising  from 
boiling  water.  Since  on  the  Fahrenheit  scale  there  are  180  de- 
grees between  the  two  fixed  points,  and  on  the  centigrade  scale 
there  are  100  degrees  between  the  same  points,  one  Fahrenheit 
degree  represents  five-ninths  of  the  temperature  interval  repre- 
sented by  one  centigrade  degree. 


4  .    STANDARD  TEMPERATURE  SCALES 

Thus,  in  Fig.  1  let  PR  represent  the  temperature  interval  be- 
tween the  two  fixed  points  of  the  centigrade  scale,  and  XZ  the 


0 
X 

tc 
Y 

100 

z 

FIG.  1. 


same  interval  on  the  Fahrenheit  scale.  A  given  temperature 
would  be  represented  according  to  the  centigrade  scale  by  tc  and 
and  according  to  the  Fahrenheit  scale  by  t/. 


Now 


PQ 
XY 


PR 
XZ 


or 


whence 
and 


(1) 

(2) 


4.  The  Thermodynamic  Temperature  Scale.  —  A  particular 
property  of  a  particular  substance  might  be  arbitrarily  adopted 
as  a  standard  of  comparison,  as  for  example,  the  relative  expan- 
sion of  mercury  in  glass,  or  the  change  of  resistance  of  platinum. 
But  it  is  highly  desirable  to  have  a  standard  temperature  scale 
that  is  independent  of  the  substance  employed. 

Carnot  discovered  that  in  the  case  of  a  reversible  thermody- 
namic  engine,  the  ratio  between  the  quantity  of  heat  absorbed 
and  the  quantity  of  heat  emitted  is  independent  of  the  working 
substance  and  depends  only  upon  the  temperatures  between 
which  the  engine  is  operating.  Lord  Kelvin  has  shown  that  this 
fact  can  be  utilized  in  the  construction  of  a  temperature  scale 
that  is  independent  of  the  medium  employed. 


THE  IDEAL  GAS  TEMPERATURE  SCALE        5 

According  to  the  Thermodynamic  Temperature  Scale,  the  ratio 
between  two  temperatures  equals  the  ratio  between  the  quantity  of 
heat  that  would  be  absorbed  and  the  quantity  that  would  be  emitted 
by  a  reversible  thermodynamic  engine  working  between  the  given 
temperatures. 

The  zero  of  the  thermodynamic  scale  is  the  temperature  which 
the  exhaust  of  a  reversible  engine  would  need  to  have  in  order 
that  the  engine  convert  into  work  all  the  heat  supplied  to  it.  It 
is  the  temperature  at  which  the  working  substance  is  devoid  of 
heat.  For  this  reason,  the  thermodynamic  zero  is  usually  called 
the  absolute  zero  of  temperature.  It  is  found  that  the  tempera- 
ture of  melting  ice  expressed  in  centigrade  degrees  on  the  ther- 
modynamic scale  is  about  273.7°C.  on  the  thermodynamic  scale. 

If,  when  two  bodies  are  in  contact  and  shielded  from  outside 
thermal  disturbance  neither  body  gains  or  loses  heat,  the  two 
bodies  are  said  to  be  in  thermal  equilibrium  with  one  another. 
According  to  the  thermodynamic  temperature  scale,  two  bodies 
in  thermal  equilibrium  are  at  the  same  temperature. 

5.  The  Ideal  Gas  Temperature  Scale.  —  All  gases  obey  the 
laws  of  Boyle  and  Charles  for  limited  ranges  of  pressures  and 
temperatures.  For  these  ranges  gases  are  said  to  be  " ideal"  or 
"perfect."  The  properties  of  perfect  gases  are  so  simple  and 
their  departure  from  the  properties  of  actual  gases  are  so  readily 
obtained  that  they  occupy  an  important  place  in  physics. 

From  the  fundamental  law  of  perfect  gases, 

pv  =  RmT, 

it  follows  that  by  reckoning  temperatures  from  a  point  about 
273.7  centigrade  degrees  below  the  melting  point  of  ice,  the  tem- 
perature of  a  fixed  mass  of  perfect  gas  at  constant  volume  varies 
directly  with  the  pressure.  This  furnishes  an  "ideal  gas"  tem- 
perature scale.  According  to  the  Ideal  Gas  Temperature  Scale, 
the  ratio  between  two  temperatures  equals  the  ratio  between  the  pres- 
sures of  a  fixed  mass  of  ideal  gas  at  constant  volume  when  at  the 
given  temperatures. 
It  can  be  shown  theoretically  that  temperatures  expressed 


6 


STANDARD  TEMPERATURE  SCALES 


according  to  the  Ideal  Gas  Scale  are  represented  by  the  same 
numbers  when  expressed  on  the  Thermodynamic  Scale. 

Bodies  that  are  in  thermal  equilibrium  with  one  another  are 
at  the  same  Ideal  Gas  Temperature. 

After  determining  the  departure  of  the  properties  of  an  actual 

gas  from  the  properties 
of  an  ideal  gas,  an  actual 
gas  can  be  used  as  the 
thermometric  substance 
and  the  results  reduced 
to  the  ideal  gas  temper- 
ature scale.  The  partic- 
ular gas  selected  to  be 
the  standard  thermomet- 
ric substance  should  be 
one  that  can  be  readily 
obtained  at  any  time  or 
place,  and  whose  physi- 
cal character  does  not 
alter  throughout  a  wide 
range  of  pressures  and 
temperatures.  Hydrogen 
fulfills  these  requirements 
and  has  been  adopted  as 
the  standard  thermomet- 
ric substance. 

6.  The  Normal  Ther- 
mometer, adopted  as  the 
standard  instrument  for 
the  comparison  of  tem- 

FlG  2  peratures    according    to 

the  Ideal  Gas  Temper- 
ature Scale,  is  a  constant  volume  hydrogen  thermometer  with  the 
gas  under  a  pressure  of  1000  mm.  of  mercury  at  the  temperature 
of  melting  ice.  On  account  of  the  danger  of  the  hydrogen 
diffusing  through  the  material  of  the  bulb  at  high  temperatures, 


THE  NORMAL  THERMOMETER  7 

the  normal  thermometer  is  seldom  used  above  300°  C.  From 
temperatures  from  300°  C.  to  1550°  C.  the  constant  volume 
nitrogen  thermometer  is  more  reliable  than  the  normal  thermom- 
eter. In  practice,  however,  the  gas  thermometer  is  employed 
only  to  standardize  some  form  of  instrument  that  is  easier  to 
operate. 

Only  at  temperatures  above  1000°  C.  is  the  departure  of  the 
Normal  Hydrogen  Scale  so  much  as  one  degree  centigrade  from 
the  Ideal  Gas  Scale.  When  necessary,  the  proper  correction 
can  be  made. 

The  normal  thermometer  in  the  Physics  Laboratory  of  Purdue 
University  is  illustrated  in  Fig.  2.  It  consists  of  a  bulb  B,  made 
of  either  quartz  or  an  alloy  of  platinum  and  rhodium.  The 
capillary  stem  is  joined  to  the  open  manometer  M.  The  bulb  is 
enclosed  in  an  electrically  heated  furnace  F,  which  is  protected 
from  outside  thermal  disturbances  by  means  of  a  water  jacket 
through  which  flows  a  steady  stream  of  water. 

By  adjusting  the  plunger  P  so  that  the  mercury  in  the  manom- 
eter M  is  maintained  at  the  fiducial  mark  a  the  volume  of  the 
gas  in  the  bulb  is  kept  at  a  definite  value. 

The  bulb  and  the  furnace  are  filled  with  either  hydrogen  or 
nitrogen.  If  the  pressure  of  the  gas  inside  the  bulb  were  differ- 
ent from  the  outside,  there  would  be  danger  of  a  change  of  vol- 
ume of  the  bulb.  By  means  of  the  plunger  PI  and  manometer 
Mi,  the  pressure  of  the  gas  outside  the  bulb  is  maintained  equal 
to  that  inside. 

There  is  no  actual  temperature-measuring  instrument  whose 
action  is  based  upon  the  principle  of  the  thermodynamic  scale. 
But  experiments  upon  hydrogen  and  nitrogen,  together  with 
the  properties  of  the  thermodynamic  scale,  show  that  throughout 
a  wide  range  of  temperatures  the  indications  of  a  constant  vol- 
ume thermometer  in  which  these  gases  are  employed  give  very 
nearly  thermodynamic  temperatures.  The  corrections  to  be 
applied  at  various  temperatures  as  determined  by  Callendar 
are  as  follows: 


8 


STANDARD  TEMPERATURE  SCALES 


Temp.,  °  C. 

Hydrogen,  °  C. 

Nitrogen,  °  C. 

-    100 

+0.005 

+0.080 

0 

+0.000 

+0.000 

+  200 

+0.0024 

+0.035 

+  450 

+0.013 

+0.189 

+1000 

+0.044 

+0.646 

7.  The  Black-body  Temperature  Scale.  —  Any  body  at  a 
temperature  above  the  absolute  zero  radiates  energy  at  a  rate 
which  depends  only  upon  the  temperature  of  the  body  and  upon 
the  nature  of  its  surface.  If  the  nature  of  the  surface  is  con- 
stant, the  temperatures  of  bodies  can  be  compared  in  terms  of 
their  radiance. 

Experience  shows  that  the  rate  at  which  a  surface  radiates, 
due  to  purely  thermal  causes,  is  proportional  to  the  rate  at  which 
it  absorbs  the  same  kind  of  energy.  That  is,  a  perfect  absorber 
would  be  a  perfect  radiator.  A  body  that  absorbs  all  the  radi- 
ance incident  upon  it  —  not  reflecting  any  or  transmitting  any  — 
is  called  a  black-body.  A  black-body  is  a  perfect  radiator,  and  all 
black-bodies  at  the  same  temperature  radiate  at  the  same  rate. 
It  follows  that  the  temperature  of  black-bodies  can  be  compared 
by  means  of  their  thermal  radiation. 

It  has  been  shown  by  Stefan  and  Boltzmann  that  the  rate 
with  which  energy  due  to  thermal  causes  is  radiated  by  a  black- 
body  is  proportional  to  the  fourth  power  of  the  thermodynamic 
temperature.  This  furnishes  a  means  of  determining  the  ther- 
modynamic temperatures  of  black-bodies  which  may  be  either 
inaccessible,  or  so  hot  that  an  instrument  could  not  safely  be 
placed  in  contact  with  them. 

If  the  body  be  nonblack,  the  rate  with  which  energy  is  radi- 
ated will  not  be  proportional  to  the  fourth  power  of  the  tempera- 
ture according  to  the  thermodynamic  scale.  But  we  can  construct 
a  scale  such  that  the  fourth  power  of  the  temperature  according 
to  this  new  scale  shall  be  proportional  to  the  rate  with  which 
energy  is  radiated  by  the  body.  This  so-called  Black-body 
Temperature  Scale  is  of  great  importance  in  expressing  tern- 


THE  BLACK-BODY  TEMPERATURE  SCALE  9 

peratures  of  bodies  that  are  either  inaccessible  or  too  hot  for 
an  instrument  to  be  placed  in  contact.  According  to  the  Black- 
body  Temperature  Scale,  when  the  energy  radiated  from  two  sur- 
faces is  due  to  purely  thermal  causes,  the  ratio  between  the  tempera- 
tures of  these  surfaces  equals  the  fourth  root  of  the  ratio  between  the 
rates  of  radiation  per  unit  area  from  the  surfaces. 

Two  bodies  will  be  at  the  same  black-body  temperature  when 
the  rate  of  their  radiation  per  unit  surface  is  the  same.  In  the 
present  and  succeeding  pages  only  radiance  due  to  purely  ther- 
mal causes  is  considered.  Radiance  due  to  chemical  or  lumi- 
nescent causes  is  excluded. 

A  piece  of  retort  carbon  absorbs  almost  all  of  the  radiance, 
of  whatever  frequency,  incident  upon  it.  Consequently  retort 
carbon  is  nearly  black.  A  piece  of  polished  platinum  absorbs 
partially,  but  to  practically  the  same  extent,  radiance  of  all 
frequencies.  Consequently  polished  platinum  is  gray.  A  lump 
of  gold  absorbs  nearly  all  the  radiance  incident  upon  it  with  the 
exception  of  the  waves  that  produce  the  visual  sensation  we 
call  yellow.  This  selective  absorption  of  gold  is  described  by 
the  statement  that  gold  is  yellow.  If  pieces  of  retort  carbon, 
polished  platinum  and  gold  be  placed  together  within  a  uni- 
formly heated  enclosure  until  they  are  in  thermal  equilibrium 
and  be  then  withdrawn,  it  will  be  found  that  the  carbon  will 
radiate  at  a  greater  rate  than  the  platinum  or  gold.  That  is, 
although  all  three  bodies  are  at  the  same  temperature  according 
to  either  the  thermodynamic  or  the  ideal  gas  scales,  they  are 
at  different  black-body  temperatures. 

Bodies,  either  black  or  nonblack,  emitting  radiance  per  unit 
area  at  the  same  rate  are  at  the  same  black-body  temperature: 
and  if  they  are  in  thermal  equilibrium  with  one  another  they  are 
at  a  common  thermodynamic  temperature.  In  the  case  of  a 
black-body  the  same  number  that  expresses  its  thermodynamic 
temperature  also  expresses  its  black-body  temperature.  But 
since  a  nonblack  body  at  the  given  thermodynamic  temperature 
radiates  less  than  a  black-body  at  the  same  thermodynamic 
temperature,  the  number  which  expresses  the  black-body  tern- 


10  STANDARD  TEMPERATURE  SCALES 

perature  of    a  nonblack-body  is  less  than    the  number  which 
expresses  its  thermodynamic  temperature. 

8.  The  Application  of  the  Three  Standard  Temperature 
Scales.  —  To  meet  various  specific  industrial  requirements, 
thermometers  have  been  devised  and  are  in  successful  use  that 
depend  upon  the  expansion  of  one  metal  relative  to  another,  the 
relative  expansion  of  a  liquid  and  the  containing  tube,  the  re- 
sistance of  a  wire,  the  change  in  electromotive  force  developed 
by  heat,  the  rate  of  emission  of  radiant  energy  by  the  hot  body, 
the  brightness  of  the  luminous  energy  of  a  selected  wave  length 
emitted  by  the  heated  body.  But  for  any  work  of  precision,  a 
thermometer  of  any  type  is  calibrated  in  terms  of  the  normal 
thermometer.  This  instrument  has  been  adopted  as  the  stand- 
ard thermometer.  But  on  account  of  its  size  and  the  care  re- 
quired in  its  operation,  it  is  not  used  in  industrial  processes,  but 
only  for  the  calibration  of  more  convenient  instruments.  The 
normal  thermometer  indications  can  be  reduced  to  the  ideal  gas 
temperature  scale. 

In  work  of  precision  all  temperatures  are  expressed  according 
to  the  thermodynamic  temperature  scale.  There  is  no  ther- 
mometer whose  action  is  based  upon  the  principle  of  this  scale. 
But  it  can  be  shown  that  the  thermodynamic  scale  is  identical 
with  the  ideal  gas  scale.  Now  any  thermometer  that  can  be 
placed  in  contact  with  the  bodies  whose  temperatures  are  sought, 
and  remain  till  it  is  in  thermal  equilibrium  with  its  surroundings, 
can  be  calibrated  directly  with  a  normal  thermometer  and  the 
indicated  temperatures  reduced  to  the  ideal  gas  temperature 
scale.  These  ideal  gas  temperatures  equal  the  thermodynamic 
temperatures. 

In  many  cases,  however,  due  either  to  the  inaccessibility  or 
high  temperature  of  a  body,  a  thermometer  cannot  be  brought 
into  thermal  equilibrium  with  the  body  whose  temperature  is 
sought.  Recourse  must  then  be  had  to  the  energy  radiated  by 
the  body  and  received  by  a  suitable  measuring  instrument.  Let 
such  an  instrument  be  directed  toward  a  black-body  that  can 
be  raised  to  a  series  of  known  thermodynamic  temperatures. 


THREE  STANDARD  TEMPERATURE  SCALES  11 

• 

From  a  series  of  readings  of  the  instrument  corresponding  to 
known  thermodynamic  temperatures  of  the  hot  body,  a  cali- 
bration curve  for  the  instrument  can  be  constructed.  This  curve 
will  give  the  thermodynamic  temperature  corresponding  to  any 
reading  of  the  instrument  within  the  range  of  the  calibration 
when  the  instrument  is  directed  toward  a  black-body.  When 
the  instrument  is  directed  toward  a  nonblack-body,  the  same 
calibration  curve  will  give,  not  thermodynamic  temperatures, 
but  black-body  temperatures. 

Since  a  nonblack-body  radiates  at  a  less  rate  than  a  black- 
body,  it  follows  that  the  number  which  represents  any  tempera- 
ture according  to  the  black-body  scale  is  smaller  than  the  number 
which  represents  the  same  temperature  on  the  thermodynamic 
scale.  The  difference  between  the  two  numbers  depends  upon 
the  departure  of  the  radiation  of  the  given  body  from  that  of 
a  black-body.  This  departure  is  a  matter  of  the  surface  of  the 
body.  If  the  radiation  coefficient  of  the  surface  be  known,  the 
thermodynamic  temperature  corresponding  to  any  black-body 
temperature  can  be  determined.  In  few  cases,  unfortunately, 
is  the  radiation  coefficient  available.  From  black-body  tem- 
peratures of  two  bodies  of  unknown  radiation  coefficients  we 
can  infer  little  with  regard  to  the  relative  thermodynamic  tem- 
peratures of  the  bodies.  For  example,  when  a  specimen  of 
carbon  and  one  of  platinum  are  at  the  same  black-body  tempera- 
ture 1500°  C.,  the  thermodynamic  temperature  of  platinum  will 
be  about  180°  C.  greater  than  that  of  the  carbon. 


CHAPTER  II 
RESISTANCE  PYROMETRY 

9.  Relation  Between  Resistance  and  Temperature.  —  Since 
the  electrical  resistance  of  most  metals  varies  continuously  with 
the  temperature  according  to  definite  laws,  and  since  the  accurate 
measurement   of   resistance   is   attended   with   no    considerable 
difficulty,   thermometers    depending   upon  this  property  are   in 
common  use  for  measuring  high  and  low  temperatures.     To  be 
available  for  such  .use,  the  metal  must  have  always  the  same 
resistivity  when  at  the  same  temperature,  and  its  temperature- 
resistance  coefficient  should  be  large.     Platinum  may  be  used 
from  the  lowest  temperatures  up  to  1100°  C.     For  temperatures 
below  200°  C.  pure  nickel  is  usually  employed. 

It  has  been  shown  by  experiment  that  if  RQ  represent  the  resist- 
ance of  a  piece  of  pure  platinum  or  of  pure  nickel  or  of  certain 
other  metals,  when  at  0°  C.,  then  the  resistance  at  t°  C.,  is  expres- 
sible by  the  equation: 

Rt  =  RQ  (1  +  at  +  fa2).  (3) 

when  a  and  b  are  constant  quantities.  These  three  constants  can 
be  determined  from  the  resistance  of  the  wire  at  three  known 
temperatures. 

10.  The  Wheatstone  Bridge.  —  It  is  easily  shown  that  in  the 
case  of  a  circuit  containing  resistances  Ri,  R2,  Rs,  and  R*,  joined  to 
a  battery  and  galvanometer  as  represented  in  Fig.  3,  there  is  no 
current  in  the  galvanometer  when 

^1  =  ^ .  (4) 

RZ     R* 

Thus,  if  any  three  of  the  resistances  are  known,  then  when  no 
current  flows  through  the  galvanometer,  the  remaining  unknown 

12 


THE  WHEATSTONE  BRIDGE 


13 


resistance  can  be  determined.  This  is  the  most  common  method 
of  measuring  resistances. 

For  general  resistance  measurements,  a  Wheatstone  bridge 
having  three  groups  of  coils  of  known  resistances,  with  convenient 
arrangements  for  altering  the  resist- 
ance of  each  group,  is  usually  em- 
ployed. For  laboratory  use,  the  box 
containing  the  coils  is  separate  from 
the  galvanometer  and  battery.  For 
shop  use  where  portability  is  essen- 
tial, the  coils,  the  galvanometer  and 
battery  are  enclosed  in  a  single  box. 
In  the  arrangement  of  the  tops  of 

the  boxes  of  coils  there  is  great  variety.  In  some,  the  resistances 
are  changed  by  means  of  plugs,  and  in  others  by  means  of  sliding 
switches.  The  top  of  a  common  form  of  cheap  box  of  coils  is 
shown  in  Fig.  4.  The  lettering  on  this  plan  corresponds  with  that 


FIG.  4. 

in  the  diagrams  Figs.  3  and  5.  In  this  model,  when  there  is 
balance  with  the  gaps  Y  and  Yr  filled  by  plugs,  and  the  gaps  X 
and  X'  open,  we  have 

RI      Rs 


14 


RESISTANCE  PYROMETRY 


whereas  with  the  gaps  Y  and  Y'  open,  and  the  gaps  X  and  X' 
filled  by  plugs,  the  resistances  #1  and  R*  will  be  interchanged  so 
that 


Rl 


By  this  switching  device  the  box 
requires  two  less  coils  than  other- 
wise would  be  needed. 


FIG.  5. 


FIG.  6. 


The  plan  of  a  box  top  in  which  rotating  switches  are  used 
instead  of  plugs  is  shown  in  Fig.  6. 

11.  Direct  Reading  Resistance  Pyrometers.  —  One  of  the 
many  forms  of  self-contained  Wheatstone  bridge  designed  to  give 
temperatures  without  computation,  from  a  single  setting,  is 

illustrated  in  Fig.  7  and  Fig.  8.  In 
this  device  the  resistance  of  the  arms 
AD  and  DC  are  equal  and  fixed  in 
value.  The  terminals  ra,  n,  and  C  of 
the  lead  wires  from  the  pyrometer 
coil  are  connected  into  the  bridge  as 
shown.  The  lead  wires  Bm,  Bn,  and 
pC  are  made  of  the  same  material 
as  the  pyrometer  coil  Bp,  and  the  resistances  of  Bm  and  pC  are 
equal.  The  resistance  of  the  arm  of  the  bridge  containing  the 
lead  wire  mB  can  be  continuously  varied  by  rotating  the  contact 
arm  qs  over  the  circle  of  wire  oqx. 


FIG. 


RESISTANCE  PYROMETERS  TO  INDUSTRIAL  USE         15 

Suppose  that  when  the  contact  point  q  is  at  o,  the  bridge  is  in 
balance.  When  the  pyrometer  coil  rises  in  temperature  its 
resistance  will  increase,  and  to  produce  a  new  balance  the  contact 
arm  must  be  rotated  in  the  clockwise  direction.  The  circle  can 
be  divided  into  spaces  and  so  marked  that  when  the  bridge  is  hi 
balance,  the  contact  arm  will  point  to  the  number  that  indicates 
the  temperature  of  the  resistance  bulb. 


FIG.  8. 

For  example,  suppose  an  instrument  is  to  be  made  that  shall 
indicate  directly  temperatures  from  0°  C.  to  200°  C.  In  this 
case  the  resistance  of  the  coil  Ao  is  made  such  that  when  the 
contact  point  q  coincides  with  o,  the  resistance  of  the  bridge  arm 
AB  equals  the  resistance  of  the  bridge  arm  BC  when  the  pyrometer 
bulb  is  at  0°  C.,  and  the  resistance  of  the  circle  of  wire  oqx  equals 
the  increase  in  the  resistance  of  the  pyrometer  coil  at  200°  C.  over 
its  resistance  at  0°  C.  As  the  change  in  the  resistance  of  the 
pyrometer  coil  is  not  directly  proportional  to  the  change  of  tem- 
peratures, the  spaces  between  marks  on  the  circular  scale  that 
indicate  equal  temperature  intervals  will  not  be  equal. 

12.  The  Availability  of  Resistance  Pyrometers  to  Industrial 
Use.  —  In  the  hands  of  trained  observers  the  platinum  resistance 
pyrometer  is  capable  of  a  precision  within  one  degree  centigrade 
from  the  lowest  temperatures  up  to  900°  C.  This  is  superior  to 
the  precision  obtainable  by  any  other  type  of  pyrometer.  But 
such  precision  should  not  be  expected  of  resistance  pyrometers- 


16  RESISTANCE  PYROMETRY 

manufactured  for  industrial  use,  especially  in  the  hands  of  ordinary 
observers. 

To  avoid  strains  within  the  resistance  coil,  the  pyrometer  bulb 
should  be  installed  so  as  to  hang  vertically  and  be  free  from  danger 
of  mechanical  injury.  The  coil  must  be  protected  from  furnace 
gases  by  an  impervious  bulb.  The  indicator  should  be  as  carefully 
treated  as  a  clock  or  other  instrument  of  equal  delicacy. 

The  outfit  should  be  frequently  tested.  It  is  not  safe  to  assume 
that  when  received  from  the  maker  the  scale  gives  correct  indica- 
tions, nor  that  the  indicators  will  remain  constant  throughout  any 
extended  period  of  time.  For  instruments  having  a  range  from 
0°  C.  to  200°  or  300°  C.,  it  will  usually  be 'sufficient  to  check  two 
points  only:  for  example,  the  0°  C.  and  the  100°  C.  point  by  means 
of  melting  ice  and  the  steam  from  boiling  water  under  a  barometric 
pressure  of  76  cm.  of  mercury.  Subsequent  testing  is  facilitated 
by  the  use  of  a  set  of  coils  that  have  resistances  equal  to  that  of 
the  pyrometer  coil  at  various  temperatures.  For  example,  at  the 
temperature  of  melting  ice  the  checking  coils  might  have  the  same 
resistance  as  the  pyrometer  coil  when  at  0°,  50°,  100°,  etc.,  respec- 
tively. Then  on  substituting  for  the  pyrometer  coil  one  of  the 
checking  coils,  the  pyrometer  indicator  should  point  to  the  number 
marked  on  the  checking  coil. 

The  resistance  pyrometer  is  especially  adapted  to  the  measure- 
ment of  temperatures  with  considerable  precision  that  vary 
through  narrow  limits,  in  situations  where  the  pyrometer  bulb  is 
in  little  danger  from  mechanical  injury.  The  causes  which  have 
thus  far  limited  the  use  of  the  instrument  are  the  fragility  of  the 
pyrometer  resistance  coil  and  the  rather  complicated  indicating 
device.  In  cases  in  which  the  required  degree  of  precision  is  not 
better  than  10°  C.,  the  base  metal  thermoelectric  pyrometer  would 
be  selected.  While  in  cases  in  which  the  "fire  end"  can  be 
shielded  from  mechanical  danger  and  the  degree  of  precision  must 
be  better  than  10°  C.,  the  resistance  pyrometer  would  be  selected. 

13.  Recording  Resistance  Pyrometers.  —  By  arranging  a 
Wheatstone  bridge  so  that  changes  in  the  resistance  of  a  pyrometer 
coil  produce  proportional  changes  in  the  position  of  some  part  of 


RECORDING  RESISTANCE  PYROMETERS  17 

the  apparatus  which  are  automatically  marked  at  regular  intervals 
of  time  on  a  piece  of  paper,  a  permanent  record  can  be  produced 
of  the  temperatures  of  the  pyrometer  coil  at  different  instants 
throughout  an  extended  period.  One  successful  instrument  of 
this  type,  designed  by  the  Leeds  and 
Northrup  Co.,  will  now  be  described. 

The  bridge  net  includes  the  pyrometer 
coil  #3,  Fig.  9,  and  the  coils  of  fixed  re-  *      * 


sistance  Bx,  yz,  and  dC,  together  with 
two  slide-wire  resistances  xy  and  zd.  On 
these  slide-wires  move  the  contact  arms 
OA  and  OD.  These  contact  arms  are 
connected  rigidly  so  that  they  move  as  a  unit.  The  diameters  of 
the  slide  wires  and  the  resistances  of  the  coils  connected  to  them 
are  such  that  the  resistance  R2  between  the  slide  contacts  A  and  D 
always  equals  the  resistance  Ri  between  A  and  B.  With  Ri  always 
equal  to  R2  whatever  the  position  of  the  sliding  contacts,  it  follows 
that  the  galvanometer  will  give  zero  deflection  when  the  resistance 
RI  between  D  and  C  equals  the  resistance  -K3  of  the  arm  BC  contain- 
ing the  pyrometer  coil.  Then,  if  with  the  pyrometer  coil  at  any 
selected  temperature  the  bridge  is  in  balance  when  the  contact 
D  is  at  D',  any  subsequent  change  in  the  temperature  of  the 
pyrometer  coil  will  be  measured  by  the  angle  D'OD  through  which 
the  contact  arm  OD  must  be  moved  to  reattain  a  balance.  It 
remains  to  describe  the  device  for  automatically  rotating  the 
contact  arms  the  proper  amount  to  bring  the  galvanometer  to  the 
zero  position,  and  the  device  for  automatically  recording  this 
amount. 

By  means  of  a  wheel  A,  Fig.  10,  the  shaft  of  which  is  connected 
to  the  contact  arms  OA  and  OD,  Fig.  9,  the  Wheatstone  bridge 
can  be  brought  to  balance.  The  direction  and  the  amount  of 
rotation  of  the  wheel  A  is  regulated  by  the  position  of  the  clutch 
arm  BBf  with  reference  to  the  cams  C  and  C"  on  the  motor-driven 
shaft  DD'. 

For  example,  with  the  clutch  arm  engaged  with  the  wheel  in  the 
position  shown  in  Fig.  10,  the  rotation  of  the  cam  C'  will  cause  the 


18 


RESISTANCE  PYROMETRY 


wheel  to  rotate  a  certain  amount  in  the  clockwise  direction, 
thereby  producing  an  equal  change  in  the  position  of  the  contact 
arms  of  the  Wheatstone  bridge.  The  clutch  arm  BB'  connected 
to  the  rocker  arm  E,  is  brought  into  engagement  with  the  wheel 
A,  and  released,  once  in  every  revolution  of  the  cam  F  on  the 


FIG.  10. 


FIG.  11. 


motor-driven  shaft  DD'.  The  position  of  the  clutch  arm  is  deter- 
mined by  the  lack  of  balance  of  the  Wheatstone  bridge.  When  the 
bridge  is  balanced,  that  is,  when  there  is  zero  current  in  the  sus- 
pended galvanometer  coil  G,  the  galvanometer  pointer  lies  directly 
below  the  gap  between  the  ends  of  the  right-angle  pieces  H  and 
H'  pivoted  at  I  and  /'  respectively.  When  the  bridge  is  out  of 
balance,  there  is  a  current  in  the  galvanometer,  and  the  galvanom- 
eter pointer  lies  somewhere  between  the  rocker  E  and  the  two 
right-angle  pieces  H  and  Hf.  Once  during  each  revolution  of  the 
motor-driven  shaft  DDf,  the  cam  J  raises  the  rocker  E.  If,  at 
that  instant  the  Wheatstone  bridge  is  not  in  balance,  that  is,  if 
the  galvanometer  pointer  is  not  below  the  gap  between  H  and  #', 


RECORDING  RESISTANCE  PYROMETERS  19 

the  rocker  E  will  push  the  galvanometer  pointer  against  the 
horizontal  position  of  one  of  the  right-angle  pieces  H  or  H '.  Being 
pivoted  at  /  and  /',  the  vertical  position  of  the  disturbed  right-angle 
piece  will  push  against  the  pin  K  or  K'  and  the  clutch  arm  will 
be  displaced  as  shown  in  Fig.  11.  The  amount  of  displacement 
of  the  clutch  arm  depends  upon  the  distance  between  the  gal- 
vanometer needle  and  the  pivot  of  the  right-angle  piece,  that  is, 
upon  the  amount  of  lack  of  balance  of  the  bridge.  The  direction 
of  displacement  depends  upon  the  direction  of  the  galvanometer 
deflection. 


FIG.  12. 

The  angular  displacements  of  the  wheel  necessary  to  rebalance 
the  Wheatstone  bridge  can  be  transformed  into  linear  displace- 
ments by  means  of  a  cord  wrapped  about  two  pulleys  L  and  Z/, 
Fig.  12.  A  pen  M  attached  to  this  cord  follows  the  variations  of 
the  resistance,  and  hence  the  temperature  of  the  pyrometer  coil. 
The  paper  under  the  pen  is  drawn  along  at  a  uniform  rate  by 
means  of  clockwork.  Thus  the  pen  automatically  traces  on  the 
paper  a  curve  coordinating  the  temperature  of  the  pyrometer  coil 
and  time. 


20  RESISTANCE  PYROMETRY 

By  substituting  a  type  wheel  and  ink  ribbon  for  the  pen,  and 
adding  a  motor  driven  multiple  point  switch,  the  instrument  just 
described  may  be  arranged  to  record  the  temperatures  of  several 
different  pyrometer  coils.  When  the  switch  has  brought  the 
galvanometer  into  connection  with  pyrometer  coil  No.  1,  the  type 
wheel  turns  a  "  1  "  toward  the  paper  and  stamps  on  the  paper  a 
dot  with  a  figure  "1"  beside  it.  One  minute  later  the  switch 
connects  the  galvanometer  to  pyrometer  coil  No.  2,  the  type 
wheel  turns  a  "2"  toward  the  paper  and  stamps  on  the  paper  a 
dot  with  a  figure  "2"  beside  it.  After  a  record  has  been  made  of 
the  temperatures  of  all  the  pyrometer  coils,  the  cycle  is  repeated. 
The  record  for  pyrometer  coil  No.  1,  consists  of  a  series  of  dots 
with  a  figure  "  1  "  alongside  of  each  dot.  The  record  for  pyrometer 
coil  No.  2  consists  of  a  series  of  dots  with  a  "2"  alongside  of  each 
dot,  and  so  on.  If  the  multiple  switch  is  arranged  for  eight 
pyrometer  coils,  eight  minutes  will  elapse  between  successive 
points  on  the  curve  for  any  given  pyrometer  coil.  It  thus  appears 
that  this  multiple  record  is  not  available  for  recording  rapid 
variations  of  temperature. 

Exp.  1.  Calibration  of  a  Resistance  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts  (9-10).  The 
object  of  this  experiment  is  to  construct  a  calibration  curve 
coordinating  temperatures  and  resistances  of  a  resistance  pyrom- 
eter from  experimentally  determined  values  of  the  resistance  at 
three  known  temperatures.  A  calibration  extending  from  0°  C. 
to  about  450°  C.,  may  be  made  from  the  freezing  point  of  water 
and  the  well-known  boiling  points  of  easily  obtained  substances. 


^stance, 

Water  .....................................  100°  C. 

Naphthalene  ................................  219°  C. 

Benzophenone  ..............................  306°  C. 

Sulphur  ....................................  445°  C. 

If  the  resistance  of  a  wire  at  temperatures  £1°  C.,  t2°  C.,  and 
C.,  be  Ri,  R2,  and  Rs,  respectively,  then  we  may  write  (3), 


CALIBRATION  OF  A  RESISTANCE  PYROMETER  21 

#1  =  #o  (1+  ati  +  W), 
£2  =  #o  (1  +  at*  +  Uf), 
Rs  =  Ro(l  +  at,  +  btf). 

Knowing  the  three  resistances  Rit  R2,  and  R3  of  the  wire  at  tem- 
peratures tit  k,  and  t3)  respectively,  the  constants  RQ)  a  and  b  can 
be  determined.  After  substituting  the  values  of  the  three  con- 
stants in  (3)  the  equation  thereby  obtained  can  be  used  for  the 
computation  of  values  of  R  corresponding  to  any  assumed  tem- 
peratures. From  a  series  of  values  of  resistances  and  correspond- 
ing temperatures,  a  curve  can  be  plotted.  This  will  be  the  re- 
quired calibration  curve  of  the  particular  resistance  pyrometer 
under  investigation. 

MANIPULATION.  —  The  resistance  pyrometer  consists  of  a  coil 
of  fine  wire  enclosed  in  a  suitable  bulb,  with  lead  wires  joined  to 
binding  posts  on  the  outside  of  the  bulb.  To  eliminate  any  error 
due  to  uncertainty  regarding  the  temperature  of  the  lead  wires, 
provision  must  be  made  to  ob- 
tain the  resistance  of  the  coil 
alone.  For  example,  the  coil 
may  be  arranged  as  in  Fig.  13, 

£ IG»    lo. 

with  a      dummy  lead,"  mB, 

joined  to  one  end  of  the  coil.  The  three  leads  nB,  mB,  Cp,  are 
of  the  same  length,  material,  and  resistance.  The  resistance  of 
the  coil  alone  can  be  obtained  by  subtracting  from  the  resistance 
between  n  and  C,  the  resistance  between  m  and  n. 

Fill  a  small  can  with  pieces  of  ice  no  larger  than  a  pea,  and  cover 
the  ice  with  water.  Immerse  the  resistance  pyrometer  bulb  in 
this  bath  of  melting  ice. 

Connect  the  galvanic  cell,  galvanometer  and  unknown  resist- 
ance to  the  Wheatstone  bridge,  using  short  thick  wires  to  connect 
the  unknown  resistance.  First,  with  the  ratio  arms  equal,  adjust 
the  rheostat  arm  until  the  galvanometer  gives  the  minimum 
deflection  on  closing  the  battery  key  and  then  the  galvanometer 
key.  This  adjustment  is  complete  when,  on  changing  the  resist- 
ance of  the  rheostat  arm  by  one  ohm  in  one  direction  the  gal- 


22 


RESISTANCE  PYROMETRY 


vanometer  deflection  is  increased,  while  on  changing  the  resistance 
by  one  ohm  in  the  other  direction  the  galvanometer  deflection 
is  reversed.  From  the  values  of  the  resistances  of  the  rheostat 
and  ratio  arms,  the  approximate  resistance  of  the  specimen  can 
be  determined  by  (4).  Knowing  the  approximate  value  of  the 
resistance,  determine  the  setting  of  the  ratio  arms  that  will  make 
the  rheostat  arm  read  to  four  digits  and  find  the  more  accurate 
value  of  the  resistance. 


FIG.  14. 


FIG.  15. 


Proceeding  in  the  same  manner  find  the  resistance  of  the  coil 
when  in  the  steam  from  water  boiling  under  an  atmospheric 
pressure  of  76  centimeters  of  mercury,  and  also  when  in  the  vapor 
from  sulphur  boiling  under  the  same  barometric  pressure.  In 
making  these  resistance  measurements  one  must  press  the  keys 
for  the  shortest  possible  time  else  the  resistance  coil  will  be  appreci- 
ably heated  by  the  passage  of  the  current. 

To  obtain  the  boiling  point  of  water  a  vessel  such  as  is  illustrated 
in  Fig.  14  is  very  satisfactory.  By  means  of  the  water  manom- 
eter M,  any  difference  of  pressure  between  the  steam  inside  and 
the  air  outside  can  be  observed.  If  the  barometric  pressure  be 


CALIBRATION  OF  A  RESISTANCE  PYROMETER  23 

H  millimeters  of  mercury  and  the  manometer  indicates  a  pressure 
of  d  millimeters  of  water,  or  (d  -f-  13.6)  millimeters  of  mercury, 
then  the  total  pressure  on  the  surface  of  the  boiling  water  is 
H  +  (d  -r-  13.6)  millimeters  of  mercury.  The  temperature  of 
the  vapor  of  water  boiling  under  various  pressures  is  given  in 
Table  1. 

To  obtain  the  boiling  point  of  sulphur  the  apparatus  illustrated 
in  Fig.  15  is  convenient.  The  sulphur  is  contained  in  an  alumin- 
ium tube  heated  by  a  current-carrying  conductor.  To  prevent 
drops  of  liquid  sulphur  that  condense  on  the  upper  part  of  the 
pyrometer  tube  from  running  down  over  the  bulb,  as  well  as  to 
diminish  the  loss  of  heat  by  radiation,  the  pyrometer  bulb  is 
enclosed  in  a  thin  aluminium  shield. 

If  the  pyrometer  bulb  be  of  quartz  or  porcelain  it  will  require 
considerable  time  for  the  coil  to  attain  the  temperature  of  the  ice, 
steam  or  sulphur  vapor.  After  the  bulb  has  been  immersed,  take 
resistance  readings  till  they  remain  constant  for  five  minutes. 
These  constant  values  are  the  ones  to  be  used  in  the  computation. 

From  the  values  of  the  three  resistances  determined  at  the 
three  known  temperatures,  compute  the  three  constants  in  (3). 
Substitute  the  values  of  these  three  constants  in  (3),  and  by  means 
of  the  empirical  equation  thereby  obtained,  compute  the  resist- 
ances of  the  coil  at  various  temperatures  at  100°  intervals  through- 
out the  range  the  pyrometer  is  to  be  employed.  With  these 
values  of  temperature  as  abscissas,  and  resistances  as  ordinates, 
plot  the  calibration  curve  of  the  given  resistance  pyrometer. 


CHAPTER  III 
THERMOELECTRIC  PYROMETRY 

14.  The  Seebeck  Effect.  —  Seebeck  discovered  that  a  junction 
of  two  dissimilar  metals  is  the  seat  of  an  electromotive  force. 
A  complete  circuit  consisting  of  wires  of  two  dissimilar  metals 
contains  two  junctions  and  two  opposing  electromotive  forces. 
If  the  entire  circuit  is  at  the  same  temperature  the  electromotive 
forces  at  the  two  junctions  will  be  equal  and  opposite,  whereas 
if  one  junction  is  at  a  higher  temperature  than  the  other  there 
will  be  a  resultant  electromotive  force  which  will  cause  a  current 
in  the  circuit.  The  magnitude  of  the  resultant  electromotive 
force  depends  upon  three  factors: 

(a)    The  nature  of  the  metals; 

(6)    The  difference  of  temperature  of  the  two  junctions; 

(c)    The  actual  temperature  of  the  two  junctions. 

As  an  example  of  the  dependence  of  the  resultant  electromotive 
force  upon  the  nature  of  the  metals,  measurements  show  that 
with  the  cold  junction  at  0°  C.,  and  the  hot  junction  at  100°  C., 
thermoelements  consisting  of  one  wire  of  pure  platinum  and  the 
other  of  the  following  substances  develop  electromotive  forces  as 
given  below: 

Microvolts.* 

Iron 2100 

Hard  steel 1800 

Nickel  steel  (0.05  Ni) 0 

Nickel  steel  (0.035  Ni) -2700 

Nickel  steel  (0.75  Ni) -3700 

Nickel 2200 

*  Micro  =  millionth. 

As  an  example  of  the  dependence  of  the  resultant  electromotive 
force  upon  the  difference  of  temperature  of  the  two  junctions, 

24 


APPLICATION  TO  TEMPERATURE  MEASUREMENT        25 

measurements  show  that  in  the  case  of  a  thermoelement  con- 
sisting of  platinum  and  an  alloy  of  platinum  with  10  per  cent 
rhodium,  with  one  junction  maintained  at  0°  C.,  there  will  be 
developed  the  following  electromotive  forces  when  the  other 
junction  has  the  temperature  assigned. 

0  C.  Microvolts. 

400 3,240 

600 5,210 

800 7,320 

1000 9,570 

1200 11,950 

1400 14,460 

1600 17,110 

That  the  resultant  electromotive  force  depends  not  only  upon 
the  difference  of  temperature  of  the  junctions  but  also  depends 
upon  the  actual  temperature  of  the  two  junctions  can  be  illus- 
trated by  the  following  experiment.  Let  the  two  ends  of  an  iron 
wire  be  joined  by  copper  wires  to  a  suitable  voltmeter.  Let  one 
copper-iron  junction  be  maintained  at  0°  C.,  while  the  other  is 
gradually  raised  in  temperature  to  600°  C.,  or  more.  The  volt- 
meter will  indicate  an  electromotive  force  which  increases  till 
the  hot  junction  is  about  275°  C.  When  the  hotter  junction 
passes  this  temperature  the  electromotive  force  decreases.  This 
phenomenon  is  called  thermoelectric  inversion,  and  the  point  of 
inversion  is  called  the  neutral  temperature.  When  the  tempera- 
ture of  the  hot  junction  becomes  about  550°  C.,  the  resultant 
electromotive  force  becomes  zero.  On  increasing  the  tempera- 
ture above  this  value  the  magnitude  of  the  resultant  electromo- 
tive force  increases  in  the  reverse  direction.  When  one  junction 
is  at  a  temperature  as  much  above  the  neutral  temperature  as 
the  temperature  of  the  other  junction  is  below  it,  the  resultant 
electromotive  force  is  zero. 

It  is  probable  that  thermoelectric  couples  of  all  elements  have 
neutral  points,  though  in  many  cases  they  are  outside  the  range 
of  temperatures  of  ordinary  experiment. 

15.  Application  to  Temperature  Measurement.  —  Since  the 
resultant  electromotive  force  of  a  thermoelectric  couple  is  a 


26  THERMOELECTRIC  PYROMETRY 

function  of  temperature,  temperatures  can  be  compared  by 
means  of  thermoelectric  couples.  A  thermoelectric  pyrometer  con- 
sists of  a  thermoelectric  couple  together  with  some  device  for 
measuring  electromotive  force.  Electromotive  forces  are  accu- 
rately compared  by  means  of  a  potentiometer,  but  are  much  more 
conveniently  compared  by  means  of  a  millivoltmeter.  As  milli- 
voltmeters  of  sufficient  accuracy  for  all  industrial  requirements 
can  be  easily  obtained  and  can  be  calibrated  so  as  to  indicate 
temperature  directly,  potentiometers  are  less  often  employed. 

A  thermoelectric  pyrometer  should  meet  the  following  re- 
quirements : 

(a)  The  resultant  electromotive  force  developed  by  the  thermo- 
electric couple  should  increase  with  rise  of  temperature  according 
to  a  known  law.  A  couple  that  produces  an  electromotive  force 
which  varies  directly  with  temperature  difference  of  its  junctions 
would  be  most  desirable. 

(6)  The  materials  composing  the  thermoelectric  couple  must 
be  chemically  and  physically  homogeneous,  and  must  be  chemi- 
cally and  physically  unaltered  under  the  conditions  of  use. 

(c)  In  case  a  millivoltmeter  indicator  is  used,  the  temperature- 
resistance    coefficient    of   the   materials    composing    the    couple 
should  be  small.     Otherwise  the  " immersion  error"  due  to  a 
change  of  resistance  with  change  of  temperature  of  the  couple 
will  be  appreciable.     This  immersion  error  is  obviated  by  the 
use  of  a  potentiometer  indicator  instead  of  a  millivoltmeter. 

(d)  The  voltmeter  should  have  a  nearly  uniform  scale  and 
sufficient  sensitiveness. 

(e)  The  resistance  of  the  voltmeter  compared  to  that  of  the 
couple  and  leads  must  be  so  great  that  the  indications  will  not 
be  appreciably  altered  by  whatever  fluctuations  may  occur  in 
the  resistance  of  the  circuit. 

(/)  The  wires  composing  the  couple  and  the  leads  must  be  of 
sufficiently  small  cross  section  to  prevent  the  junction  being 
appreciably  cooled  by  conduction  of  heat  from  it. 

16.  Choice  of  Metals  for  Thermoelectric  Couples.  —  The 
limit  of  the  ratio  of  the  electromotive  force  developed  by  a  couple 


CHOICE  OF  METALS  FOR  THERMOELECTRIC  COUPLES     27 

to  the  difference  of  temperature  of  its  two  junctions  is  called  the 
thermoelectric  power  of  the  couple.  It  is  usually  expressed  in 
microvolts  per  degree  centigrade. 

Many  metals  undergo  a  molecular  transformation  within  cer- 
tain ranges  of  temperature.  Within  these  temperature  limits 
such  a  metal  is  not  available  for  use  in  a  thermoelectric  couple. 
For  instance,  nickel  undergoes  a  molecular  transformation  be- 
tween 230°  C.  and  390°  C.  which  causes  its  thermoelectric  power 
and  also  its  resistance  to  depart  throughout  this  interval  from 
the  normal  trend.  Nickel  may  be  used  in  a  thermoelectric 
element  from  400°  C.,  to  900°  C. 

A  wire  that  is  ununiformly  hard  throughout  its  length  will  pro- 
duce parasitic  currents  when  uniformly  heated.  Careful  anneal- 
ing will  correct  this  fault.  Wires  of  iron,  nickel,  palladium,  and 
their  alloys  when  heated  to  certain  temperatures  give  rise  to 
parasitic  currents  which  render  them  unfit,  at  these  temperatures, 
for  use  in  thermoelectric  elements. 

At  about  700°  C.,  iron,  steel,  nickel,  and  copper  become  so 
brittle  as  to  render  their  use  inconvenient  above  this  temperature. 

As  the  metals  of  the  platinum  group  can  be  heated  above 
1400°  C.  without  melting,  and  they  have  no  neutral  temperature 
within  the  range  of  ordinary  experiment,  and  as  their  alloys  can 
be  made  physically  and  chemically  homogeneous,  these  metals 
were  early  used  for  the  construction  of  thermoelectric  pyrometers. 
Care  -must  be  exercised,  however,  not  to  keep  them  long  at  a 
temperature  above  1100°  C.,  or  they  will  become  crystalline 
and  brittle.  And  care  must  be  taken  that  they  be  not  heated  in 
a  space  containing  volatile  metals,  or  their  chemical  composi- 
tion will  be  altered,  thereby  changing  their  thermoelectric  power. 
With  proper  precautions  a  thermoelectric  element  consisting  of  a 
pure  platinum  wire  in  connection  with  a  wire  of  an  alloy  of  plati- 
num with  ten  per  cent  rhodium,  is  thoroughly  satisfactory  for 
measuring  temperatures  from  the  lowest  obtainable  up  to  about 
1400°  C. 

The  great  cost  of  platinum  and  rhodium,  however,  has  limited 
the  adoption  of  the  (Pt  —  .90  Pt  .10  Rh)  element  for  industrial 


28  THERMOELECTRIC  PYROMETRY 

use.  Much  research  has  been  devoted  to  the  discovery  of  alloys 
of  cheaper  metals  that  would  be  suited  to  industrial  measure- 
ments. Many  so-called  "base  metal"  couples  have  been  devised 
that  have  proved  of  great  value  in  technical  operations. 

A  couple  in  considerable  use  has  for  the  positive  wire  an  alloy 
which  analysis  shows  to  consist  of  Cu  58.78,  Ni  40.70,  and 
slight  impurities,  while  the  negative  wire  is  of  iron  with  slight 
impurities. 

For  temperatures  up  to  1300°  C.,  a  certain  pyrometer  maker 
uses  for  the  positive  wire  an  alloy  which  analysis  shows  to  con- 
sist of  Ni  97.28,  Si  2.15,  Fe  0.35,  Al  0.15:  and  for  the  negative 
wire  an  alloy  consisting  of  Ni  88.67,  Cr  10.75,  Al  0.22,  Si  0.15, 
Fe  0.10.  For  lower  temperatures  the  same  negative  wire  is 
employed  in  connection  with  a  positive  wire  consisting  of  Ni  45.0, 
Cr55.0. 

Many  base  metal  couples  have  a  much  higher  thermoelectric 
power  than  the  platinum-rhodioplatinum  couple  and  so  can  be 
used  in  connection  with  more  robust  millivoltmeters.  They  have 
the  disadvantages,  however,  of  less  uniform  thermoelectric  power, 
short  life,  and  restricted  temperature  range. 

17.  The  Construction  of  a  Thermoelectric  Couple.  —  The 
ends  of  the  two  wires  constituting  the  hot  junction  should  be 
fused  together.  The  fusion  may  be  readily  accomplished  by 
means  of  an  oxyhydrogen  flame,  an  oxyacetylene  flame,  or  an 
electric  arc.  Before  use  a  couple  should  be  annealed.  This  may 
be  accomplished  by  raising  the  entire  length  to  redness  by  means 
of  an  electric  current  and  then,  depending  upon  the  nature  of 
the  metals,  either  quenching  in  water  or  allowing  it  to  slowly  cool. 

The  two  wires  constituting  the  couple  should  be  insulated 
throughout  their  length.  For  temperatures  below  1200°  C.,  this 
may  be  accomplished  by  small  quartz  tubes  or  by  a  covering  of 
purified  asbestos  string.  For  higher  temperatures  it  may  be 
accomplished  by  means  of  beads  or  tubes  of  hard  porcelain. 

For  ordinary  use  the  insulated  wire  constituting  the  "fire  end" 
should  be  protected  against  chemical  and  mechanical  injury  by  a 
sheath  of  iron,  a  chrome-nickel  alloy,  quartz,  or  Marquardt  por- 


MILLIVOLTMETER  INDICATORS  29 

celain.  An  iron  sheath  should  not  be  used  for  temperatures 
above  800°  C.  Fused  quartz  will  not  break  by  sudden  change 
of  temperature  and  is  available  for  temperatures  up  to  1200°  C. 
Above  this  temperature,  however,  quartz  gradually  devitrifies 
and  crumbles.  Marquardt  porcelain  can  be  used  up  to  1600°  C., 
if  not  heated  or  cooled  so  quickly  as  to  crack. 

Instead  of  two  parallel  wires,  insulated  from  one  another  and 
enclosed  in  a  protecting  sheath,  certain  base  metal  couples  con- 
sist of  a  rod  of  one  metal  placed  axially  within  a  tube  of  the  other 
metal,  with  the  rod  and  tube  fused  together  at  one  end.  Unless 
placed  in  some  substance  that  will  attack  the  material  of  the 
tube,  such  a  cane-like  "pyod"  requires  no  protecting  sheath. 

18.  Indicators-for  Thermoelectric  Pyrometers.  —  The  electro- 
motive forces  developed  by  a  thermoelectric  couple  are  measured 
either  by  a  millivoltmeter  or  by  a  potentiometer.     From  a  cali- 
bration curve  constructed  from  a  given  cold-junction  tempera- 
ture, the  scale  of  the  millivoltmeter  or  potentiometer  can  be  so 
divided  that  the  instrument  will  indicate  directly  the  temperature 
of  the  hot  junction.     A  millivoltmeter  or  potentiometer  with  a 
scale  divided  so  as  to  indicate  temperatures  directly  is  called  a 
thermoelectric  pyrometer  indicator.     The  scale  of  a  thermoelec- 
tric pyrometer  indicator  can  be  used  only  in  connection  with  the 
thermo  couple  with  which  it  was  calibrated,  or  with  one  constructed 
of  the  same  materials. 

19.  Millivoltmeter    Indicators.  —  Thermoelectric    pyrometer 
indicators  are  usually  moving-coil  millivoltmeters  of  considerable 
sensitiveness  and  fairly  robust  construction.     In  the  most  sensi- 
tive type,  the  coil  is  supported,  above  and  below,  by  very  thin 
metal  wires.     The  most  common  method  of  support  is  by  two 
jeweled  bearings.     Another  successful  method  of  support  is  by 
a  single  jeweled  bearing  at  the  center  of  the  coil. 

The  electric  resistance  of  a  millivoltmeter  should  be  so  high 
compared  to  that  of  the  remainder  of  the  circuit,  that  the  read- 
ings will  not  be  appreciably  altered  by  changes  in  the  resistance 
of  the  circuit  produced  by  temperature  fluctuations.  The  resist- 
ance that  the  indicator  must  have  in  order  that  the  potential 


30  THERMOELECTRIC  PYROMETRY 

difference  at  its  terminals  may  not  vary  more  than  a  given  amount 
when  the  resistance  of  the  remainder  of  the  circuit  is  altered 
can  be  readily  found.  Thus,  letting  E  represent  the  resultant 
electromotive  force  of  the  couple,  and  ri}  r2,  r3,  the  resistance  of 

the  couple,  the  connecting  leads  and 
the  indicator,  respectively,  there  will 
be  a  current  /  throughout  the  circuit 
given  by  the  equation: 


7  = 


FIG.  16.  +  ra  +  r3 

The  electromotive  force  of  the  couple 

develops  a  potential  difference  V,  at  the  terminals  of  the  indi- 
cator of  a  magnitude  given  by  the  equation  : 

r-t. 

rs 

Equating  the  right-hand  members  of  these  equations 
V  _          E 
rs      r\  +  r2  +  r3 

V=         ^\     .  (5) 

ri  +  r2  +  r3 

Problem.  —  Assuming  that  the  temperatures  of  the  hot  and  of  the  cold 
junction  remain  constant,  and  also  that  the  resistance  of  the  millivoltmeter 
remains  constant,  find  the  resistance  that  the  millivoltmeter  must  have  in 
order  that  the  potential  difference  at  its  terminals  may  not  change  more  than 
one  per  cent  when  the  resistance  of  the  remainder  of  the  circuit  changes  from 
2  ohms  to  3  ohms. 

Solution.  —  Since  the  temperature  of  each  junction  remains  constant,  the 
resultant  electromotive  force  E  will  remain  constant.  Now  when  n  +  r2  =  2, 
we  have  (5), 

F-2TS'  (6) 

And  since,  when  n  +  r2  =  3,  the  potential  difference  at  the  terminal  of  the  indi- 
cator is  to  be  0.99  V,  we  may  write  (5), 

(7) 


Solving  for  r3  by  dividing  each  member  of  (7)  by  the  corresponding  member  of 
(6),  we  find  the  required  resistance  of  the  indicator  to  be 

r3  =  97  ohms. 


THE  POTENTIOMETER  METHOD  31 

In  millivoltmeters  designed  for  use  in  connection  with  thermo- 
electric pyrometers,  two  general  methods  are  in  vogue  for  the 
prevention  of  changes  in  the  indications  being  produced  by 
fluctuations  in  the  temperature  of  the  indicator. 

First,  by  the  use  of  coils  of  zero  temperature-resistance  co- 
efficient. As  all  alloys  of  negligible  or  negative  temperature 
coefficient  have  a  high  resistivity,  it  is  customary  to  use  a  moving 
coil  of  about  10  ohms  made  of  copper,  in  series  with  a  multiplier, 
of  not  less  than  100  ohms  made  of  manganin  or  other  alloy  of 
zero  or  negative  temperature  coefficient. 

Second,  by  properly  altering  the  magnetic  flux  in  the  region 
occupied  by  the  moving  coil.  If  this  flux  be  increased  by  the 
proper  amount  when  the  resistance  of  the  coils  of  the  indicator 
is  increased,  the  indications  will  be  unaffected  by  temperature 
changes.  This  result  is  accomplished  automatically  in  the 
Thwing  pyrometer  millivoltmeters  by  a  diminution  of  the  air 
gap  when  the  temperature  rises. 

20.  The  Potentiometer  Method  of  Measuring  Electromotive 
Forces.  —  Electromotive  forces  can  be  measured  with  greater 
precision  by  means  of  the  potentiometer  method  than  by  means 
of  a  millivoltmeter.  Though  the  measurement  of  an  electro- 
motive force  by  means  of  a  potentiometer  involves  an  adjust- 
ment, whereas  the  millivoltmeter  is  direct  reading,  instruments 
are  now  available  for  use  with  thermoelectric  couples,  in  which 
this  adjustment  is  very  easily  made. 

The  rationale  of  the  potentiometer  method  will  be  rendered 
clear  by  a  consideration  of  the  following  diagrams : 

Working  Battery 


FIG.  17.  FIG.  18. 

Consider  a  circuit  consisting  of  a  conductor  ABCDF,  Fig.  17, 
joined  to  the  terminals  of  a  battery  maintained  at  constant  elec- 


32  THERMOELECTRIC  PYROMETRY 

tromotive  force.  Suppose  a  line  including  the  thermocouple  T 
whose  electromotive  force  is  required,  a  galvanometer  G,  key  K, 
and  sliding  contact  E,  to  be  connected  into  the  circuit  ABCDF, 
as  shown.  If  the  electromotive  force  of  the  thermoelectric  couple 
is  in  the  direction  to  oppose  the  potential  difference  at  the  points 
D  and  E  due  to  the  battery,  a  position  of  the  sliding  contact  E 
can  be  found  such  that  the  potential  difference  between  D  and  E 
due  to  the  battery  is  equal  and  opposite  to  the  potential  differ- 
ence between  the  same  points  due  to  the  thermoelectric  couple. 
The  balance  will  be  indicated  by  zero  deflection  of  the  galva- 
nometer when  the  key  K  is  closed.  This  potential  difference  can 
be  determined  by  substituting  for  the  thermoelectric  couple  a 
cell  of  known  and  constant  electromotive  force,  and  rebalancing 
by  moving  the  sliding  contact  to  some  point  Ef.  Thus  if  the 
current  in  the  main  circuit  be  I  the  resistance  between  D  and  E 
be  R,  that  between  D  and  E'  be  R',  the  potential  difference  be- 
tween D  and  E  be  V,  and  that  between  D  and  E'  be  V't  we  have, 
when  the  thermoelectric  couple  is  in  place 


and  when  the  standard  cell  takes  the  place  of  the  thermoelectric 
couple, 

V' 


V      R 

V'  =  R'' 

Since  the  thermoelectric  couple  produces  no  current  when  the 
potentiometer  is  in  balance,  its  electromotive  force  E  numeri- 
cally equals  the  potential  difference  V.  And,  since  the  standard 
cell  produces  no  current  when  the  potentiometer  is  in  balance, 
its  electromotive  force  Ef  numerically  equals  the  potential 
difference  V. 

K-l-l- 

If  the  slide  wire  be  uniform,  the  resistance  between  any  two 


THE  POTENTIOMETER  METHOD  33 

points  will  be  proportional  to  the  length  between  those  points. 
Denoting  the  length  DE  by  I,  and  the  length  DE'  by  V 


=  _ 
Rf      I'' 


and  the  previous  equation  becomes 


Since  for  a  particular  wire  and  standard  cell,  —  is  a  constant 

L 

quantity,  which  we  may  denote  by  c 

E  =  d.  (8) 

Knowing  the  constant  c,  the  whole  slide  wire  can  be  marked  off 
so  as  to  indicate  directly  the  electromotive  forces  corresponding 
to  various  points  of  the  wire.  So  long  as  the  battery  between 
A  and  F  has  a  constant  electromotive  force,  any  electromotive 
force  E,  within  the  range  of  the  instrument,  will  be  indicated 
by  the  position  of  the  sliding  contact  when  a  balance  is  effected. 
Though  there  are  cells,  which  if  used  in  series  with  a  high 
resistance  for  but  a  few  seconds  at  a  time,  maintain  electromotive 
forces  at  a  constant  value  through  a  period  of  several  years,  no 
actual  battery  maintains  a  constant  electromotive  force  if  sup- 
plying appreciable  current  for  a  long  time.  Consequently,  the 
ideal  arrangement  diagrammed  in  Fig.  17  must  be  modified  for 
practical  use.  Fig.  18  shows  the  addition  of  an  adjustable  re- 
sistance H  to  the  main  circuit,  and  a  standard  cell  with  a  high 
resistance  and  a  switch  82  shunted  about  a  portion  of  the  main 
circuit.  The  purpose  of  the  standard  cell  is  to  check  the  poten- 
tial difference  between  B  and  C.  In  case  this  potential  difference 
has  not  the  required  value,  it  can  be  regulated  by  varying  the 
adjustable  resistance  H.  In  using  this  apparatus,  the  current  in 
the  main  line  is  regulated  till  on  closing  the  switch  Sz  the  gal- 
vanometer gives  zero  deflection.  The  apparatus  can  be  cali- 
brated by  means  of  another  standard  cell  as  described  in  the 
preceding  paragraph.  Thereafter,  before  taking  a  set  of  readings, 
the  current  in  the  main  line  is  first  adjusted  till  on  closing  the 


34 


THERMOELECTRIC  PYROMETRY 


Working  Battery 
A 


switch  S2  the  galvanometer  gives  zero  deflection;  then  with  $2 
open,  the  sliding  contact  E  is  moved  back  and  forth  till  on  closing 
the  switch  Si,  the  galvanometer  gives  zero  deflection.  The 
required  electromotive  force  is  then  read  from  the  scale  beside 
the  calibrated  slide  wire. 

21.  Potentiometer  Indicators  for  Thermoelectric  Pyrometers. 
—  For  a  given  length  of  slide-wire,  greater  sensitiveness  is  ob- 
tained by  throwing  a  shunt  XY, 
about  the  slide-wire,  as  shown  in 
Fig.  19. 

This  arrangement  is  used  fre- 
quently in  potentiometer  indica- 
tors for  thermoelectric  pyrometers. 
The  cold-junction  error  may  be 
compensated  by  the  operator  slid- 
ing the  galvanometer  connection  D,  one  way  or  the  other  by  a 
predetermined  amount  depending  upon  the  departure  of  the  tem- 
perature of  the  cold  end  from  the  value  when  calibrated.  .The 
top  of  a  commercial  potentiometer  indicator  arranged  in  this 
manner  is  illustrated  in  Fig.  20.  In  this  figure,  H'  is  a  knob 


FIG.  20. 

connected  to  the  sliding  contact  of  the  variable  resistance  H, 
Fig.  19,  which  regulates  the  current  in  the  main  circuit;  E'  is 
a  knob  to  adjust  the  position  of  the  contact  E  on  the  slide  wire; 
D'  is  a  knob  to  adjust  the  position  of  the  galvanometer  contact 
D  on  the  slide  wire. 


THE  DEFLECTION  POTENTIOMETER        35 


To  use  the  cold-junction  compensator  D,  one  must  have  a 
temperature-electromotive  force  calibration  curve  of  the  par- 
ticular thermocouple  being  used,  for  a  certain  fixed  temperature 
to  of  the  cold  junction.  This  curve  indicates  the  electromotive 
force  Ec  that  would  be  developed  if  the  cold  junction  were  at 
to  and  the  hot  junction  were  at  any  temperature  tc.  If  in  sub- 
sequent use,  the  cold  junction  be  at  tc  instead  of  at  to,  the  tem- 
perature, of  the  hot  junction  is  that  corresponding  to  the  sum  of 
Ec  and  that  actually  developed  by  the  couple.  Hence,  by  setting 
the  cold-junction  compensator  at  Ec,  the  balance  position  of  the 
sliding  contact  E  will  give  the  electromotive  force  that  would  be 
produced  if  the  cold  junction  were  at  fo  and  the  hot  junction  were 
at  its  present  temperature. 

Potentiometer  indicators  are  usually  calibrated  to  read  in 
millivolts.  Such  can  be  used  in  connection  with  any  calibrated 
thermocouple.  If,  however,  an  indicator  is  to  be  used  in  con- 
nection with  only  thermocouples  composed  of  the  same  two 
metals,  it  can  be  marked  so  as  to  indicate  temperatures  directly. 

Instead  of  adjusting  by  hand  the  position  of  the  sliding  con- 
tact D,  the  cold-junction  error  can  be  automatically  compen- 
sated by  the  use  of  a  wire  N,  Fig.  19,  of  proper  resistance  made 
of  a  material  whose  temperature-resistance  curve  is  of  the  same 
shape  as  the  temperature-electromotive  force  curve  of  the  ther- 
mocouple. In  connection  with  thermocouples  having  a  straight 
line  calibration  curve  from  0°  C.  to  about  50°  C.,  nickel  can  be 
used  for  the  coil  N.  As  in  the  simple  potentiometer,  care  must 
be  taken  to  keep  the  potential  difference  between  B  and  C  con- 
stant. If  the  resistance  of  the  nickel  wire  should  change,  the 
potential  difference  between  B  and  C  will  change. 

22.  The  Deflection  Potentiometer.  —  When  the  electromotive 
force  of  a  thermocouple  is  measured  by  means  of  a  potentiometer 
of  the  ordinary  type,  a  balance  must  be  obtained  for  each  read- 
ing made.  This  is  a  disadvantage  when  measuring  temperatures 
which  are  varying.  A  dead  beat  voltmeter  has  the  advantage 
of  giving  the  electromotive  force  at  any  instant  without  any 
setting.  The  voltmeter,  however,  is  not  so  accurate  as  the  po- 


36 


THERMOELECTRIC  PYROMETRY 


tentiometer  and  the  readings  are  affected  by  changes  in  the 
resistance  of  the  thermocouple  circuit. 

A  scheme  of  measurement  which  combines  the  two  methods 
is  made  use  of  in  the  deflection  potentiometer.  The  greater  part 
of  the  electromotive  force  to  be  measured  is  balanced  against  a 
known  potential  difference  as  in  the  ordinary  potentiometer  and 
the  remainder  causes  a  deflection  of  the  galvanometer  which  is 
calibrated  to  read  potential  differences.  For  a  given  required 
precision,  if  only  a  small  part  of  the  electromotive  force  be  meas- 
ured by  means  of  the  voltmeter  then  a  larger  percentage  error  in 
the  voltmeter  reading  is  allowable  than  if  all  of  the  electromotive 
force  is  read  by  the  voltmeter. 

By  means  of  the  deflection  potentiometer  the  resistance  setting 
need  not  be  exact  as  the  excess  electromotive  force  can  be  read 
from  the  voltmeter.  Thus  sudden  fluctuations  of  the  electromo- 
tive force  can  be  observed  directly  with  a  greater  accuracy  than 
is  possible  with  a  voltmeter. 

Suppose  Fig.  21  to  represent  a  potentiometer  circuit  with  a 
thermocouple  connected  for  measurement. 


M 


FIG.  21. 


FIG.  22. 


Let  E  be  the  electromotive  force  developed  by  the  thermocouple 
and  ei,  that  of  the  working  battery.  Then  if  the  balance  is  not 
complete  there  will  be  a  current  ia,  flowing  through  the  galva- 
nometer. From  Ohm's  law  its  value  will  be 


-  E 


r3 


ra  + 


fa 


r3 


, 
+ 


THE  DEFLECTION  POTENTIOMETER  37 

If  the  denominator  remains  constant  the  current  through  the 
galvanometer  is  proportional  to  the  difference  of  the  potential 
difference  across  r{  and  the  electromotive  force  to  be  measured. 
This  means  that  rg  must  be  varied  so  as  to  keep  the  sum 


constant. 


n  +  r2  -f 

The  resultant  resistance  between  A  and  D  represented  by  the 
quantity 

r>  n  (r2  +  r3) 

KAD  =  ~ 

n  +  r2  +  r3 

will  be  minimum  when  the  slider  is  at  A  or  B,  and  will  be  maxi- 
mum when  the  slider  is  at  some  intermediate  position.  Since  rg 
plus  this  quantity  must  be  maintained  constant,  it  follows  that 
rg  must  have  its  minimum  value  when  this  quantity  is  a  maximum, 
and  contrariwise. 

This  result  may  be  accomplished  by  adding  to  the  circuit  in 
Fig.  21,  two  adjustable  resistances  MN  and  EF  as  illustrated  in 
Fig.  22.  In  this  figure,  rg  may  be  considered  to  be  made  up  of 
the  resistance  of  the  voltmeter  and  a  portion  of  the  resistance  of 
MN.  In  adjusting  the  balance  by  moving  the  slider  D  from  A 
to  B,  as  much  resistance  must  be  added  to  the  voltmeter  by  the 
wire  MN  as  is  taken  out  of  the  resultant  resistance  between  A 
and  D.  For  this  adjustment,  the  resistance  between  E  and  B, 
including  r4,  r6,  and  the  battery  (corresponding  to  r3  in  Fig.  21), 
must  be  maintained  constant. 

The  working  current  is  maintained  at  the  proper  value  by 
adjusting  the  position  of  the  slider  D\.  This  adjustment  of  the 
position  of  D\  is  without  effect  on  the  resistance  between  E  and  B. 

The  adjustment  of  the  working  current  through  AB  is  obtained 
as  in  the  ordinary  potentiometer  by  balancing  a  standard  cell 
across  a  portion  of  this  resistance.  Then  the  electromotive  force 
to  be  measured  is  connected  to  the  instrument  and  the  slider  D 
adjusted  until  the  voltmeter  pointer  remains  on  the  scale.  The 
electromotive  force  then  is  obtained  by  adding  to  the  potential 
difference  across  r\  (which  is  indicated  by  the  position  of  D),  the 


38  THERMOELECTRIC  PYROMETRY 

voltmeter  scale  reading.  The  balance  need  never  be  complete  and 
the  voltmeter  reading  will  follow  small  fluctuations  of  the  electro- 
motive force  without  an  adjustment  of  the  slider  D. 

THE  NORTHRUP  PYROVOLTER.  —  In  this  method  the  electro- 
motive force  of  the  thermoelement  is  first  balanced  against  the 
potential  difference  at  the  terminals  of  a  known  resistance  trav- 
ersed by  a  current,  and  then  this  current  is  measured  by  a  gal- 
vanometer. The  product  of  the  measured  current  and  the  con- 
stant resistance  equals  the  required  potential  difference.  The 
circuit  is  represented  in  Fig.  23.  With  the  dial  switch  R  in  the 


FIG.  23. 

position  indicated,  the  main  current  goes  from  Ba  through  the 
rheostat  Rh,  the  left-hand  side  of  the  switch,  Rg,  R  and  back  to 
the  battery.  By  joining  to  the  binding  posts  X,  in  the  proper 
direction,  the  thermoelement  whose  electromotive  force  is  re- 
quired, the  potential  difference  at  the  terminals  of  the  thermo- 
couple is  opposed  by  that  at  the  terminals  of  R.  The  current  in 
R  can  be  adjusted  by  means  of  the  rheostat  till  these  two  poten- 
tial differences  are  equal.  When  balanced,  the  galvanometer 
gives  zero  deflection. 

If  the  dial  switch  be  now  rotated  into  the  dotted  position,  the 
current  from  the  battery  traverses  Rh,  the  right-hand  part  of  the 
switch,  the  galvanometer,  and  R}  back  to  the  battery.  That  is, 
the  current  traverses  the  same  circuit  as  before  except  that  G 
takes  the  place  of  Rg.  If  the  resistance  of  G  equals  that  of  Ra, 
the  current  through  R  is  the  same  as  before.  That  is,  the  current 
through  R  when  the  two  potential  differences  were  balanced  is 


RECORDING  THERMOELECTRIC  PYROMETERS     39 

now  indicated  by  the  galvanometer.  The  product  of  the  con- 
stant resistance  R  and  the  current  producing  any  selected  deflec- 
tion can  be  marked  beside  the  selected  scale  division,  and  thus 
the  instrument  divided  so  as  to  indicate  potential  difference 
directly. 

The  precision  of  the  pyrovolter  method  is  limited  by  that  of 
the  galvanometer.  But  the  method  is  superior  to  the  voltmeter 
method  in  that  the  electromotive  force  being  measured  is  not 
altered  by  the  introduction  of  the  device;  the  indication  is  in- 
dependent of  the  resistance  of  the  lead  wires;  and  the  observed 
potential  difference  at  the  terminals  of  a  source  of  electromotive 
force  equals  the  electromotive  force. 

23.  Recording  Thermoelectric  Pyrometers.  —  A  recording 
thermoelectric  pyrometer  can  be  produced  by  substituting  for  the 
Wheatstone  bridge  and  resistance  coil  of  the  recorder  described 
in  Art.  13,  a  potentiometer  and  thermoelectric  couple  such  as  is 
diagrammed  in  Fig.  19.  In  this  case  the  slide  wire  DE,  Fig.  19, 
would  be  bent  into  a  circular  arc,  and  the  contact  point  E  would 
be  on  the  end  of  a  radial  arm  operated  by  the  shaft  of  the  wheel 
A,  Fig.  10.  The  potential  difference  between  the  points  B  and 
C,  Fig.  19,  can  be  maintained  constant  by  an  occasional  adjust- 
ment, by  hand,  of  the  control  rheostat  H.  The  apparatus  can 
also  be  arranged  so  that  this  adjustment  will  be  done  automatically. 

There  are  also  on  the  market  several  forms  of  recorders  in  which 
a  millivoltmeter  is  used  instead  of  a  potentiometer.  One  success- 
ful form  designed  by  the  Wilson-Maeulen  Co.,  is  illustrated  in 
Fig.  24.  The  record  paper  is  drawn  at  a  constant  speed  by  means 
of  clockwork  under  the  pointer  N  of  the  millivoltmeter  V.  Every 
ten  seconds  the  boom  B  chops  down  on  the  pointer.  Directly 
under  the  boom,  and  separated  from  it  only  by  the  record  paper 
and  a  typewriter  ribbon,  is  a  sharp  straight  edge.  When  the 
boom  strikes  the  pointer  a  dot  will  be  made  on  the  paper  where 
the  pointer  crosses  the  straight  edge.  The  paper  is  so  thin  that 
the  dot  shows  on  both  sides.  In  this  manner  a  curve  is  automati- 
cally drawn  coordinating  time  and  millivoltmeter  deflections. 

This  device  can  also  be  arranged  to  record  the  temperatures 


40 


THERMOELECTRIC  PYROMETRY 


of  several  different  thermoelectric  couples.  For  this  purpose 
there  is  added  a  magnetically  operated,  clock  controlled  switch, 
which  shifts  the  connection  of  the  millivoltmeter  every  80  seconds 
from  one  thermoelectric  couple  to  the  next.  As  the  successive 
dots  on  the  record  merge  into  a  line,  the  curve  for  each  thermo- 
electric couple  consists  of  a  series  of  dashes,  separated  by  spaces 
equal  to  the  product  of  the  length  of  a  dash  and  the  number  of 
thermoelectric  couples. 


FIG.  24. 

To  readily  distinguish  between  the  different  curves,  a  multiple 
color  typewriter  ribbon  is  employed  —  one  color  for  each  thermo- 
electric couple.  The  same  switch  that  shifts  the  millivoltmeter 
connection  from  one  thermoelectric  couple  to  another,  at  the  same 
time  shifts  the  typewriter  ribbon  from  one  color  to  another. 

24.  The  Cold- Junction  Correction.  —  The  resultant  electro- 
motive force  developed  by  a  given  thermoelectric  couple  depends 


THE  COLD-JUNCTION  CORRECTION 


41 


upon  the  difference  of  temperature  of  the  hot  and  cold  junctions, 
and  also  upon  the  actual  temperatures  of  the  hot  and  cold  junc- 
tions. In  calibrating  a  couple,  the  cold  junction  is  maintained 
at  some  definite  temperature  (usually  0°  C.  or  20°  C.),  the  hot 
junction  is  raised  to  known  temperatures,  and  the  electromotive 
forces  thereby  produced  are  noted.  A  calibration  curve  coordinat- 
ing temperatures  of  the  hot  junction  and  the  corresponding 
electromotive  forces  produced  when  the  cold  junction  is  at  the 
assigned  temperature  can  be  drawn. 

After  a  certain  thermoelectric  couple  has  been  calibrated,  the 
scale  of  the  millivoltmeter  used  with  it  may  be  divided  so  as  to 
indicate  temperatures  instead  of  millivolts.  Such  a  direct  read- 
ing instrument  will  give  correct  indications  only,  (a)  when  used 
with  the  thermoelectric  couple  with  which  it  was  calibrated  or 
one  with  the  same  thermoelectric  properties;  (6)  when  the  cold 
junction  of  the  thermoelectric  couple  is  at  the  temperature  main- 
tained during  calibration. 


FIG.  25. 

In  industrial  practice  it  is  often  more  convenient  to  maintain 
the  temperature  of  the  cold  junction  at  a  constant  temperature 
different  than  the  one  it  had  when  the  couple  was  calibrated.  In 
this  event  the  indicator  reading  must  be  modified  by  a  "cold-junc- 
tion correction."  In  this  article,  the  temperature  of  the  cold 
junction  is  constant,  but  is  not  the  same  as  when  the  instrument 
was  calibrated.  Two  cases  will  be  considered. 

FIRST.  —  Indicator  reading  in  Millivolts.  —  In  Fig.  25  is  shown 


42  THERMOELECTRIC  PYROMETRY 

a  curve  representing  the  relation  between  the  temperature  of  the 
hot  junction  and  the  electromotive  force  of  a  couple  having  the 
cold  junction  maintained  at  0°  C.  It  will  be  noted  that  as  zero 
electromotive  force  corresponds  to  zero  temperature  difference, 
this  curve  passes  through  the  origin  of  temperatures  and  electro- 
motive forces. 

In  the  case  of  a  thermoelectric  couple  calibrated  at  0°  C.,  when 
used  with  the  cold  junction  at  tc°,  the  temperature  of  the  hot 
junction  is  not  the  temperature  corresponding  to  the  electro- 
motive force  indicated  by  the  millivoltmeter,  but  is  the  tempera- 
ture corresponding  to  an  electromotive  force  equal  to  the  sum  of 
the  electromotive  force  indicated  by  the  millivoltmeter  (Ei,  Fig. 
25)  and  the  electromotive  force  (EC)  Fig.  25),  that  would  be 
developed  if  the  cold  junction  were  at  0°  and  the  hot  junction 
at  tc°. 

For  example,  let  it  be  required  to  determine  the  temperature  of 
the  hot  junction  corresponding  to  an  indicated  electromotive 
force  EI,  Fig.  25,  when  the  cold  junction  is  at  temperature  tc. 
Add  to  OE1}  the  distance  EiA  =  OEC.  From  A,  draw  a  line  AB 
parallel  to  the  temperature  axis  till  it  intersects  the  calibration 
curve  for  a  cold  junction  at  0°.  Project  the  latter  point  of  inter- 
section B  on  to  the  temperature  axis.  The  point  t  gives  the  re- 
quired temperature  of  the  hot  junction. 

It  will  be  seen  from  this  construction  that  if  the  calibration 
curve  be  a  straight  line,  the  cold  junction  correction  for  a  cold- 
junction  temperature  tc  is  (te  —  t0),  where  to  is  the  temperature  of 
the  cold  junction  when  the  couple  was  calibrated.  In  this  case, 
the  cold  junction  correction  is  the  same  for  all  electromotive 
forces. 

The  calibration  curve  of  most  couples,  however,  is  not  a  straight 
line.  When  the  calibration  curve  is  not  a  straight  line,  the  cold 
junction  correction  does  not  equal  (tc  —  U),  and  it  is  not  of  the 
same  magnitude  for  all  electromotive  forces. 

The  calibration  curves  of  many  base  metal  couples  are  sufficiently 
near  being  straight  lines,  that,  for  departures  from  the  standard 
cold  junction  temperatures  of  as  much  as  10°  C.,  the  error  intro- 


THE  COLD-JUNCTION  CORRECTION  43 

duced  by  assuming  the  cold  junction  correction  to  be  (tc  —  to)  is 
not  greater  than  the  error  allowable  in  industrial  practice. 

SECOND.  —  Indicator  reading  in  Degrees.  —  In  Fig.  26,  let  the 
curve  represent  the  calibration  curve  of  the  thermoelectric  pyrom- 
eter when  the  cold  junction  is  at  0°  C.  Thus,  when  the  cold 
junction  is  at  0°  C.,  and  the  hot  junction  is  at  t°  C.,  there  will  be 
developed  an  electromotive  force  E.  When  the  cold  junction  is 
at  0°  C.,  and  the  hot  junction  is  at  tc°,  there  will  be  developed  an 
electromotive  force  Ec.  When  the  cold  junction  is  at  tc°,  and  the 
hot  junction  is  at  t°  C.,  there  will  be  developed  an  electromotive 
force  Eit  such  that 

E!  =  E-  Ec.  (9) 

The  millivoltmeter  will  now  not  indicate  t°,  but  will  indicate  some 
lower  temperature  £1°.  The  difference  between  the  temperature 
of  the  hot  junction  and  the  value  indicated  on  the  millivoltmeter 
is  the  cold  junction  correction. 
That  is,  the  cold  junction  cor- 
rection, 

p  =  t  -  ti. 

The  magnitude  of  the  cold  junc- 
tion correction  p  is  now  to  be 
determined  according  to  a  method 
due  to  Paul  D.  Foote  (Bull.  Bu- 
reau of  Standards,  Vol.  9,  pp.  Fi 
553-565).  We  will  first  express 
the  values  of  t  and  ti  in  terms  of  the  corresponding  electromotive 
forces  E  and  E\.  The  thermoelectromotive  force  developed  when 
the  junctions  are  at  different  temperatures  is  a  function  of  the 
temperature  difference.  When  the  cold  junction  is  at  0°  C.,  and 
the  hot  junction  is  at  t°  C.,  there  will  be  developed  an  electro- 
motive force  having  the  value 

E=f®,  (10) 

where  the  function  /,  depends  upon  the  nature  of  the  two  metals. 
This  equation  gives  the  relation  between  the  electromotive  force 
impressed  on  the  millivoltmeter  and  the  meter  readings. 


44  THERMOELECTRIC  PYROMETRY 

When  the  cold  junction  is  at  tc°  C.,  and  the  hot  junction  at  t°  C., 
then  there  will  be  developed  an  electromotive  force  EI.  Since  the 
apparatus  is  assumed  to  be  calibrated  with  the  cold  junction  at 
0°  C.,  the  millivoltmeter  will  now  not  indicate  t°,  but  will  indicate 
a  lower  temperature  t\.  In  this  case,  since  EI  is  the  electromotive 
force  impressed  on  the  millivoltmeter,  and  h  is  the  meter  reading, 


Since  (10)  E  =  /(<),  and  (9)  E  =  #1  +  E,, 

f(t)  =  E,+  Ec. 
Expressing  temperature  explicitly  in  terms  of  EI  and  EC}  we  have 

t  =  4>(Ei  +  Ec), 

where  <£  is  the  inverse  function  of  /. 
Also,  from  (11), 

Zi  =  0  (#1).  (12) 

Consequently,  the  magnitude  of  the  cold-junction  correction 

p[=t-t1]  =  4>  (E,  +  #c)  -  0  (E,).  (13) 

Expanding  <f>  (Ei  +  Ee)  by  Taylor's  theorem, 


Whence  (12), 

.  .  .  +^d^EA 

2!     dE?  n\     dE? 

(14) 

Under  certain  experimental  conditions  this  expression  can  be 
reduced  to  a  much  simpler  form.  Thus  if  Ec  be  small  in  compari- 
son with  Ely  all  terms  involving  the  second  and  higher  powers  of 
Ec  may  be  neglected  without  sensibly  affecting  the  magnitude  of 
p.  Noting  that  the  first  and  last  terms  of  the  right-hand  member 
cancel,  the  introduction  of  this  approximation  gives  us 

.         d6  (E,)  , 

P^Ec—~"  (15) 


THE  COLD-JUNCTION  CORRECTION  45 

Differentiating  (12)  with  respect  to  dEi, 


whence  (15)  becomes 


. 

^7dJ 
\dtj 


or,  in  words,  when  the  couple  is  calibrated  with  the  cold  junction 
at  0°  C.,  and  the  couple  is  afterward  used  with  the  cold  junction 
at  tc°  C.,  the  observed  temperature  indication  must  be  increased 
by  the  quotient  obtained  by  dividing  the  electromotive  force 
generated  when  the  junctions  are  at  0°  C.,  and  tc°  C.,  respectively, 
by  the  slope  of  the  calibration  curve  at  the  apparent  temperature 
of  the  hot  junction. 

The  case  is  similar  in  which  the  thermoelectric  couple  was 
calibrated  with  the  cold  junction  not  at  0°  C.,  but  at  te'f  and  the 
couple  is  subsequently  used  with  the  cold  junction  at  te".  Thus, 
representing  by  Ec'  the  electromotive  force  generated  when  the 
junctions  are  at  tcf  and  te",  respectively,  and  by  Ec",  the  electro- 
motive force  generated  when  the  junctions  are  at  tc"  and  the 
apparent  temperature  t\,  respectively,  and  following  the  preceding 
method,  we  obtain  for  the  present  case, 

.   TJT  /    dti    _.__   EC  /•1«\ 

*-**' 


Or,  in  words,  when  the  couple  is  calibrated  with  the  cold  junction 
at  tc,  and  the  couple  is  afterward  used  with  the  cold  junction  at 
te",  the  observed  temperature  indication  must  be  increased  by 
the  quotient  obtained  by  dividing  the  electromotive  force  when 
the  junctions  are  at  tc  and  tc",  respectively,  by  the  slope  of  the 
calibration  curve  at  the  observed  apparent  temperature. 


46 


THERMOELECTRIC  PYROMETRY 


Problem.  —  In  calibrating  a  certain  thermoelectric  pyrometer  with  the  cold 
junction  maintained  at  0°  C.,  the  following  data  were  obtained: 

Indicator  deflection,  Electromotive  force, 

0  C.  microvolts. 

100 1,600 

300 5,400 

600 12,600 

900 21,600 

1100 28,600 

1300 36,400 

1400 40,600 

Construct  curves  coordinating  indicator  deflections  and  corrections  to  be 
added  when  the  cold  junction  is  at  20°  C.,  50°  C.,  70°  C.,  and  100°  C. 

Solution.  —  The  calibration  curve  for  the  cold  junction  at  0°  C.,  obtained 
by  plotting  the  above  deflections  and  electromotive  forces  is  as  shown  in 
Fig.  27. 


1400° 


FIG.  27. 


An  inspection  of  this  curve  would  suggest  to  a  person  familiar  with  the 
appearances  of  curves  and  the  forms  of  their  equations,  that  this  curve  might 
be  represented  by  an  equation  of  the  form: 

E  =  bt  +  cP  (18) 


THE  COLD-JUNCTION  CORRECTION  47 

To  find  the  values  of  the  constants  b  and  c  we  may  select  any  two  points 
of  the  curve,  for  example  (300°  C.,  5400  microvolts)  and  (1100°C.,  28600 
microvolts).  We  then  may  write: 

5400  =    3006  +  (300)2c.  (19) 

and  28,600  =  1100  b  +  (1100)2  c.  (20) 

To  eliminate  (6),  multiply  each  term  of  (24)  by  33,  and  each  term  of  (25) 
by  9.  Then, 

178,200  =  9900  b  +  2,970,000  c.  (21) 

257,400  =  9900  b  +  10,890,000  c.  (22) 

Subtracting  each  member  of  (21)  from  the  corresponding  member  of  (22), 

79,200  =  7,920,000  c, 
whence, 

c  =  0.01. 

Substituting  this  value  of  c  in  (19), 

5400  =  300  b  +  900, 
whence 

6  =  15. 

On  substituting  these  values  of  b  and  c  in  the  general  equation  (18),  the 
definite  equation  of  the  curve  is  found  to  be 

#  =  15* +  0.01*2.  (23) 

By  means  of  this  equation  the  quantities  in  the  right-hand  member  of 
(16)  can  be  found.  Thus  suppose  it  be  required  to  find  the  cold- junction 
correction  for  an  indicated  temperature  at  1000°  C.,  when  the  cold  junction 
is  at  30°  C.  From  (23) 

Ec  =  15  (30)  +  0.01  (30)2  =  459  microvolts.  (24) 

Again,  differentiating  E  in  (23)  with  respect  to  t,  we  obtain 

^  =  15+0.02*. 

For  an  indicated  temperature  *i  =  1000°  C.  we  would  have 

15  +  0.02  (1000)  =  35. 


\dtl 


1000C 


Consequently,  when  the  cold  junction  is  at  30°  the  correction  to  be  added 
to  an  indicated  temperature  of  1000°  C.,  is  (16) 


±L  /• 

— — 

dh  /1000°J 


(25) 


48 


THERMOELECTRIC  PYROMETRY 


In  the  same  manner  the  following  tables  were  computed: 


tc 

EC 

tc 

Ec 

10 

Microvolts. 

151 

°  C. 

60 

Microvolts. 

936 

20 

304 

70 

1099 

30 

459 

80 

1264 

40 

616 

90 

1431 

50 

775 

100 

1600 

< 

\dti  )ti 

* 

(f\ 

100 

17 

800 

31 

200 

19 

900 

33 

300 

21 

1000 

35 

400 

23 

1100 

37 

500 

25 

1200 

39 

600 

27 

1300 

41 

700 

29 

1400 

43 

By  substituting  these  values  in  (16), 

P  == 


the  values  in  the  following  table  were  computed, 
the  correction  "curves  for  cold  junctions  at  20°  C 
have  been  plotted  in  Fig.  28. 

80°T 


From  the  data  in  this  table 
.,  50°  C.,  70°  C.,  and  100°  C., 


700°  900 ' 

FIG.  28. 


1300' 


1500° 


COLD-JUNCTION  CORRECTION 


49 


Values  of  the  cold-junction  correction  to  be  added  to  the  temperature  readings 
•oj  a  thermoelectric  couple  which  when  the  cold  junction  is  at  0°  C.  has  a  cali- 
bration curve  of  the  jorm  E  =  15 1  +  0.01 12. 


tl 

Cold-junction  temperatures. 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

100° 

200 

7.9 

16.0 

24.2 

32.4 

40.8 

49.3 

57.9 

66.5 

75.4 

84.2 

300 

7.2 

14.5 

21.8 

29.3 

36.9 

44.6 

52.4 

60.2 

68.2 

76.3 

400 

6.6 

13.2 

19.9 

26.7 

33.7 

40.7 

47.8 

55.0 

62.4 

59.5 

500 

6.0 

12.1 

18.4 

24.6 

31.0 

37.4 

44.0 

50.7 

57.4 

64:0 

600 

5.6 

11.2 

17.0 

22.5 

28.7 

34.8 

40.8 

46.9 

53.1 

59.3 

700 

5.2 

10.5 

15.8 

21.2 

26.8 

32.3 

37.9 

43.7 

49.4 

55.2 

800 

4.9 

9.8 

14.8 

19.9 

25.0 

30.2 

35.4 

40.8 

46.2 

51.7 

900 

4.6 

9.2 

13.9 

18.7 

23.5 

28.4 

33.3 

38.4 

43.4 

48.5 

1000 

4.3 

8.7 

13.1 

17.7 

22.2 

26.8 

31.4 

36.2 

40.9 

45.7 

1100 

4.1 

8.2 

12.4 

16.7 

21.0 

25.3 

29.7 

34.2 

38.7 

43.2 

1200 

3.9 

7.8 

11.8 

15.8 

19.9 

24.0 

28.2 

32.4 

36.7 

41.0 

1300 

3.7 

7.4 

11.2 

15.0 

18.9 

22.8 

26.8 

30.9 

35.0 

39.0 

1400 

3.5 

7.1 

10.7 

14.3 

18.0 

21.8 

25.6 

29.4 

33.3 

37.2 

1500 

3.4 

6.8 

10.2 

13.7 

17.2 

20.8 

24.5 

28.1 

31.8 

35.6 

25.  Cold-junction  Correction  when  the  Temperature  of  the 
Cold  Junction  is  not  Constant.  —  If  the  temperature  of  the  cold 
junction  of  a  thermocouple  does  not  remain  constant  but  yet  can 
be  observed  at  the  same  time  that  the  indicator  reading  is  taken, 
then  the  corrections  that  must  be  applied  to  the  indicator  reading 
can  also  be  obtained.  For,  from  the  expression  for  the  correction 
(16), 


the  correction  to  be  applied  to  the  reading  will  be  proportional 
to  the  electromotive  force  developed  when  one  junction  is  at 
0°  C.,  and  the  other  is  at  the  actual  temperature  of  the  cold 
junction.  Thus,  if  at  one  time  the  cold-junction  temperature  is 
tc,  and  at  another  time  is  tc',  then  the  correction  in  the  second  case 
is  in  terms  of  that  in  the  first  case, 


50  THERMOELECTRIC  PYROMETRY 

/  T?  r\ 

However,  since  the  ratio  (  —  M  is  very  nearly  equal  to  the  ratio 

\Eic/ 

of  the  temperatures  of  the  cold  junction,  we  may  write 


(26) 

lc/ 

Then  if  we  know  the  corrections  to  be  applied  to  the  observed 
readings  when  the  cold  junction  is  at  any  temperature,  we  can 
obtain  by  a  simple  proportion  the  correction  when  the  cold-  junc- 
tion temperature  is  at  any  other  known  value. 

The  degree  of  accuracy  of  this  method  may  be  checked  from  the 
table  at  the  end  of  the  previous  article.  For  example,  check  the 
fifth  part  of  the  corrections  in  the  50°  column  with  the  values  in 
the  10°  column.  The  errors  are  less  than  1°  C. 

A  convenient  method  would  be  to  plot  corrections  against 
indicated  readings,  as  in  Fig.  28,  for  the  maximum  cold-junction 
temperature  that  would  be  attained,  and  then  interpolate.  For 
example,  suppose  that  the  curve  for  50°  C.  were  plotted.  If  the 
indicated  reading  was  500°  C.,  and  the  cold-junction  temperature 
was  30°  then  the  correction  to  be  applied  would  be  (26), 

30 


Fig.  28  shows  that  for  the  pyrometer  there  considered,  when 
tc  =  50°,  and  ti  =  500°,  pi  =  31°. 
Whence,  when  t  =  30°,  the  cold-  junction  correction  is 


Problem.  —  The  thermocouple,  the  equation  of  which  is  E  =  15  t  +  0.01  12 
when  the  temperature  of  the  cold  junction  is  0°  C.,  was  used  to  indicate  a 
series  of  temperatures  when  the  cold  junction  was  not  maintained  at  a  constant 
temperature.  The  temperatures  of  the  cold  junction  at  various  indicated 
temperatures  of  the  hot  junction  were  as  given  below.  It  is  required  to 
determine  the  actual  temperature  of  the  hot  junction  corresponding  to  the 
various  observed  indicated  temperatures. 


SHOP  METHODS  FOR  REDUCING  THE  ERRORS 


51 


Hot  junction 
(indicated). 

Cold  junction. 

Hot  junction 
(indicated). 

Cold  junction. 

200 

0  C. 
20 

°C. 
900 

°C. 
29 

300 

22 

1000 

24 

400 

25 

1100 

27 

500 

28 

1200 

30 

600 

31 

1300 

25 

700 

36 

1400 

30 

800 

32 

1500 

35 

Solution.  —  Arrange  these  data  in  two  columns  as  in  the  following  table. 
In  the  third  column  put  the  corrections  to  be  applied  if  the  cold  junction  had 
been  maintained  at  some  constant  temperature  other  than  0°.  For  this 
particular  thermocouple  such  corrections  for  various  cold-junction  constant 
temperatures  are  given  in  the  table  at  the  end  of  Art.  24.  For  the  use  of  this 
solution  the  values  for  any  particular  constant  temperature  may  be  selected. 
The  third  column  of  the  table  below  gives  the  values  for  50°  C.,  expressed  in 
the  nearest  integer.  The  values  in  the  second  and  third  columns  substituted 
in  (26)  give  the  actual  corrections  to  be  added  to  the  indicated  temperatures 
under  the  conditions  specified  in  the  present  problem.  These  corrections  are 
given  in  the  fourth  column. 


Hot  junction 
(indicated), 
h 

Cold 
junction, 
«„' 

Correction  if  cold 
junction  were  at 
50°  C., 
Pi 

Actual  correction, 

'**© 

Hot  junction 
(actual), 
I 

200 

°C. 

20 

0  C. 
41 

41  (20  -4-  50)  =  16 

216 

300 

22 

37 

37  (22  -r-  50)  =  16 

316 

400 

25 

34 

34  (25  +  50)  =  17 

417 

500 

28 

31 

31  (28  -r-  50)  =  17 

517 

600 

31 

29 

29  (31  -r-  50)  =  18 

618 

700 

36 

27 

27  (36  -r-  50)  =  19 

719 

800 

32 

25 

25  (32  -T-  50)  =  16 

816 

900 

29 

23 

23  (29  -r-  50)  =  13 

913 

1000 

24 

22 

22  (24  -T-  50)  =  11 

1011 

1100 

27 

21 

21  (27  -T-  50)  =  11 

1111 

1200 

30 

20 

20  (30  -T-  50)  =  12 

1212 

1300 

25 

19 

19  (25  -r-  50)  =  10 

1310 

1400 

30 

18 

18  (30  -T-  50)  =  11 

1411 

1500 

35 

17 

17  (35  -r  50)  =  12 

1512 

26.  Shop  Methods  for  Reducing  the  Errors  due  to  Variation 
in  the  Temperature  of  the  Cold  Junction.  —  If  the  temperature 
of  the  cold  junction  is  higher  than  it  was  when  the  pyrometer  was 
calibrated,  the  indicated  temperature  will  be  too  low;  and  if  the 


52  THERMOELECTRIC  PYROMETRY 

temperature  is  lower  than  it  was  when  the  instrument  was  cali- 
brated, the  indicated  temperature  will  be  too  high.  The  obvious 
method  to  prevent  these  errors  is  to  maintain  the  cold  junction 
at  a  constant  temperature. 

The  temperature  of  the  cold  junction  can  be  maintained  at  an 
approximately  constant  temperature  by  enclosing  it  in  a  box 
with  one  or  more  incandescent  lamps  that  are  automatically 
turned  on  or  off  by  a  thermostat  as  the  temperature  of  the  box 
falls  below  or  rises  above  a  certain  selected  value. 

The  temperature  of  the  cold  junction  can  also  be  maintained 
at  an  approximately  constant  temperature  for  a  considerable 
period  either  by  enclosing  it  in  a  jacket  through  which  flows  a 
steady  stream  of  water  from  the  city  mains,  or  by  burying  it  at 
a  depth  of  six  to  ten  feet  in  the  ground.  The  latter  method 
requires  that  the  wires  composing  the  thermocouple  shall  be  of 
considerable  length,  or  that  extension  leads  be  used  composed  of 
either  the  same  materials  as  the  wires  of  the  couple  to  which  they 
are  joined,  or  of  other  materials  of  the  same  thermoelectric  proper- 
ties. In  the  case  of  base  metal  couples  there  is  no  difficulty  in 
providing  extension  leads  of  the  same  materials  as  the  metals 
composing  the  couple;  but  in  the  case  of  the  platinum  couples  the 
expense  would  usually  be  prohibitive.  To  overcome  this  difficulty 
various  alloys  are  on  the  market  which,  through  the  range  of 
temperatures  to  which  the  cold  junction  would  be  apt  to  be 
subjected,  have  the  same  thermoelectric  properties  as  the  standard 
platinum-platinum  alloy  couples.  The  use  of  these  various  alloys 
for  extending  the  wires  of  a  couple  is  guarded  by  patents. 

For  the  degree  of  precision  required  in  commercial  practice  the 
following  methods  are  in  successful  use  for  overcoming  the  errors 
due  to  fluctuations  in  the  temperature  of  the  cold  junction  of  a 
thermoelectric  pyrometer. 

(a)  The  Use  of  a  Compensator  Couple.  —  The  cold  junction 
can,  in  effect,  be  removed  to  a  place  where  it  is  possible  to  main- 
tain the  temperature  constant  by  the  use  of  a  supplementary 
thermoelectric  couple. 

In  Fig.  29,  T  represents  a  thermoelectric  couple  employed  to 


SHOP  METHODS  FOR  REDUCING  THE  ERRORS 


53 


measure  the  difference  between  the  temperature  of  the  hot  region 
x,  and  the  cold  region  y,  maintained  at  a  constant  temperature. 
T8  is  a  supplementary  couple  of  the  same  thermoelectric  properties 
as  T.  The  two  couples  are  joined  in  opposition.  In  practice  T 
would  be  an  expensive  rhodioplatinum  couple,  and  T,  would  be 
one  composed  of  cheaper  materials.  The  ends  a,  6,  c  are  so  close 
together  that  they  will  all  be  at  a  common  temperature.  G  is  a 
millivoltmeter  or  other  indicating  instrument. 


Denote  the  temperatures  of  x,  y,  and  the  common  temperature 
of  a,  6,  c,  by  the  symbols  tx,  ty,  and  tg,  respectively.  Then  when 
tx>tz> tv,  current  flows  along  the  path  axbyc.  If  now  tn  diminishes 
while  tx  and  tv  remain  unchanged  (usually  not  equal),  the  electro- 
motive force  in  T8  will  diminish  to  the  same  extent  as  that  in  T 
increases,  thereby  leaving  the  resultant  current  in  the  circuit 
unchanged. 

If,  however,  tn  increases  while  tx  and  tv  remain  constant,  the 
electromotive  force  in  T  will  diminish  and  the  electromotive  force 
in  T,  will  increase  to  the  same  extent,  again  leaving  the  resultant 
current  unchanged. 

When  tx>ty>tz  current  flows  along  the  paths  axb  and  cyb.  If 
now  tg  diminishes  while  tx  and  ty  remain  constant,  the  electro- 
motive force  in  T  will  increase,  and  the  opposing  electromotive 
force  in  T8  will  increase  in  the  same  degree,  thereby  leaving  the 
resultant  current  in  the  circuit  unchanged.  If,  however,  tz  in- 
creases while  tx  and  ty  remain  unchanged,  the  electromotive  force 
in  T  will  diminish  and  the  opposing  electromotive  force  in  T,  will 


54  THERMOELECTRIC  PYROMETRY 

diminish  to  the  same  extent,  thereby  leaving  the  resultant  current 
in  the  circuit  unchanged. 

It  is  thus  seen  that  any  change  in  the  temperature  of  z  is  with- 
out effect  on  the  indicated  reading. 

(6)  Adjustment  of  the  Zero  Point  of  the  Millivoltmeter.  —  When 
the  thermoelectric  properties  of  the  couple  are  such  that  through- 
out the  entire  scale  of  the  indicating  instrument  equal  spaces 
correspond  to  equal  changes  of  the  temperature  of  the  hot  end  of 
the  couple,  the  correct  temperature  of  the  hot  junction  is  obtained 
by  adding  to  the  indicated  temperature  the  number  of  degrees  that 
the  cold  junction  is  hotter  than  it  was  when  the  instrument  was 
calibrated.  This  addition  or  subtraction  is  often  done  by  shifting 
the  zero  point  of  the  scale  of  the  indicator  relative  to  the  pointer 
through  the  space  corresponding  to  the  difference  between  the 
present  temperature  of  the  cold  junction  and  the  temperature 
when  the  instrument  was  calibrated.  After  this  adjustment  has 
been  made,  the  temperatures  indicated  on  the  millivoltmeter  will 
be  correct. 

When  this  method  is  employed  an  ordinary  mercury-in-glass 
thermometer  is  usually  kept  at  the  cold  junction  and  the  zero 
point  of  the  millivoltmeter  readjusted  by  hand  whenever  a  change 
in  temperature  of  the  cold  junction  occurs.  Devices  are  on  the 
market  for  automatically  changing  the  zero  point  of  the  milli- 
voltmeter when  the  temperature  of  the  cold  junction  changes. 

This  method  is  available  only  when  the  calibration  curve  co- 
ordinating hot-junction  temperatures  and  millivoltmeter  deflec- 
tions is  a  straight  line. 

(c)  Compensating  Wheatstone  Bridge.  —  In  Art.  10,  the  Wheat- 
stone  bridge  is  explained  and  the  equation  stated.  Suppose  the 
thermoelectric  pyrometer  GT  is  put  in  place  of  the  galvanometer 
of  a  Wheatstone  bridge.  When  (4) 


no  current  from  the  battery  will  flow  through  the  millivoltmeter, 
and  the  millivoltmeter  indication  will  be  due  entirely  to  the 


ADVANTAGES  AND  DISADVANTAGES  55 

difference  in  temperature  of  the  junctions  of  the  thermoelectric 
couple.  If  the  resistance  of  one  of  the  bridge  arms  is  changed, 
then  a  current  from  the  battery  will  traverse  the  millivoltmeter. 

Suppose  the  arm  BC  consists  of  wire  of  a  high  resistance- 
temperature  coefficient  and  the  three  other  arms  consist  of  wires 
of  zero  resistance-temperature  coefficient.  Then  with  the  battery 
connected  as  shown  in  the  diagram,  when  the  temperature  of  the 
Wheatstone  bridge  increases,  current  from  the  battery  will  traverse 
the  millivoltmeter  in  the  direction  BGD.  The  increase  in  tem- 
perature of  the  cold  junction  of  the  thermoelectric  couple  will  at 
the  same  time  reduce  the  current  flow-  B 

ing  through  the  millivoltmeter  due  to 
the  couple. 

It  is  thus  seen   that  by  properly  A 
selecting  the  materials  for  the  bridge 
arms,  an  arrangement  can  be  produced 
that  will  give  millivoltmeter  readings 
that  are  independent  of  the  temper-  FlG 

ature  of  the  cold  j  unc  tion.     In  practice, 

the  four  bridge  arms,  the  battery  and  the  millivoltmeter  are  en- 
closed in  one  case,  and  the  ends  of  the  thermoelectric  couple 
joined  to  terminals  on  the  case.  After  being  once  adjusted, 
there  will  be  no  cold-junction  error  so  long  as  the  electromotive 
force  of  the  battery  remains  constant. 

27.  Advantages  and  Disadvantages  of  the  Thermoelectric 
Method  of  Measuring  Temperatures.  —  This  method  is  available 
for  measuring  temperatures  from  the  boiling  point  of  liquid  air 
(-184°  C.)  up  to  1500°  C.  The  method  is  superior  to  other  high 
temperature  methods  in  the  following  respects: 

(a)   Ease  of  observation; 

(6)   Adaptability  to  a  variety  of  purposes; 

(c)  Cheapness  of  apparatus; 

(d)  Robustness  of  apparatus  and  ease  of  repair; 

(e)  Availability  for  automatically  making  a  permanent  record 
of  temperature  extending  over  a  considerable  interval  of  time. 


56  THERMOELECTRIC  PYROMETRY 

The  points  in  which  the  method  is  inferior  to  some  other  methods 
are: 

(1)  The  trouble  involved  in  making  the  cold- junction  correc- 
tion.    This  is  more  serious  when  the  range  of  temperature  is  small. 

(2)  On  account  of  the  small  electromotive  forces  produced,  very 
sensitive  milli voltmeters  are  required.     For  example,  with  the  cold 
junction  at  0°  C.,  the  electromotive  force  of  the  rhodioplatinum 
couple  is  18  millivolts  at  1600°  C.,  and  that  of  the  various  nickel 
couples  is  about  60  millivolts  at  their  highest  ranges. 

(3)  Rhodioplatinum    couples    give    diminished    electromotive 
forces  if  allowed  to  remain  long  above  1200°  C.,  or  if  employed  in 
an  atmosphere  of  contaminating  gases. 

(4)  The  high  cost  of  platinum  makes  it  necessary  to  use  small 
wires.     Such    a   thermoelectric   element   will   have   appreciably 
different  resistances  when  immersed  to  varying  depths  in  a  furnace. 
On  account  of  this  fact,  the  millivoltmeter  reading  will  depend 
upon  the  length  of  the  couple  immersed  in  the  hot  source. 

28.  The  Installation  of  Thermoelectric  Pyrometers.  —  On 
account  of  the  robustness  and  compactness  of  the  apparatus,  the 
low  cost  of  installation,  and  maintenance,  ease  of  operation,  wide 
temperature  range,  and  degree  of  precision,  the  thermoelectric 
pyrometer  is  probably  more  generally  employed  than  all  other 
classes  of  pyrometers  together.  Couples  made  of  the  platinum 
group  of  metals  can  be  used  for  short  periods  up  to  1500°  C.,  with 
a  precision  to  within  1°  C.  There  are  base  metal  couples  that 
can  be  used  up  to  1200°  C.  with  a  degree  of  precision  within  most 
industrial  requirements.  All  base  metal  couples,  however,  used 
in  measurements  that  are  required  to  be  trustworthy  within  5°  C. 
should  be  frequently  checked  against  a  rhodioplatinum  standard. 

All  couples  must  be  protected  from  oxidizing  and  reducing  gases 
or  anything  else  that  would  contaminate  the  metals  composing 
them.  For  this  purpose  are  employed  protecting  tubes  or  sheaths 
of  pure  iron,  pure  nickel,  Marquardt  mass,  fused  quartz,  chamotte, 
carborundum,  clay,  graphite,  corundite,  and  special  alloys  for 
particular  corrosive  materials.  Marquardt  mass  tubes  can  be 
used  continuously  at  temperatures  as  high  as  1300°  C.,  so  long  as 


THE  INSTALLATION  OF  THERMOELECTRIC  PYROMETERS     57 

they  are  not  subjected  to  sudden  changes  of  temperature.  If 
their  temperature  be  suddenly  changed,  they  will  crack.  They 
are  quite  unsuited  to  use  where  they  would  be  subjected  to  shoot- 
ing flames.  Fused  quartz  can  be  used  continuously  up  to  1100°  C. 
Above  1200°  C.,  quartz  devitrifies  and  crumbles,  and,  in  the 
presence  of  volatile  reducing  agents  such  as  carbon  or  hydrogen, 
forms  volatile  silicides  which  will  destroy  platinum.  Fused  quartz 
will  not  crack  when  subjected  to  a  change  of  temperature,  however 
sudden. 

Marquardt  mass  and  fused  quartz  tubes  designed  for  rough 
handling  should  be  protected  with  a  sheath  of  some  material  of 
greater  mechanical  strength.  Chamotte  sheaths  can  be  used  in 
temperatures  up  to  1500°  C.  They  are  not  broken  by  sudden 
changes  in  temperature.  They  cannot  be  used  in  molten  baths, 
nor  in  reducing  or  alkaline  gases.  Carborundum  sheaths  can  be 
used  at  very  high  temperatures,  under  both  oxidizing  and  reducing 
conditions.  Chlorine,  however,  begins  to  act  upon  carborundum 
at  about  950°  C.  Basic  slags  also  attack  it.  Clay,  graphite,  and 
corundite  sheaths  have  a  wide  application  in  brick  and  pottery 
kilns,  glass  melting  furnaces  and  large  annealing  ovens. 

To  avoid  any  bending  of  the  protecting  sheath  when  subjected 
to  high  temperatures,  the  couple  should  either  be  suspended  verti- 
cally or  supported  at  two  or  more  points. 

When  a  thermoelectric  pyrometer  is  calibrated  there  is  a  certain 
resistance  in  circuit.  If  a  millivoltmeter  indicator  is  employed, 
the  same  resistance  as  that  in  circuit  when  the  instrument  was 
calibrated  must  be  maintained  in  all  subsequent  use.  With  a 
potentiometer  indicator,  the  resistance  in  circuit  need  not  be 
constant. 

Due  regard  must  be  had  to  the  reduction  of  the  cold-junction 
error.  For  most  industrial  operations  in  which  base  metal  couples 
are  employed  it  is  sufficient  to  use  leads  of  the  same  materials  as 
the  couples,  and  either  bury  the  cold  junction  six  or  eight  feet 
under  ground,  or  surround  the  cold  junction  with  a  jacket  through 
which  flows  water  from  the  mains. 


58  THERMOELECTRIC  PYROMETRY 

Exp.  2.   Calibration  of  a  Thermoelectric  Couple 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  (14-19).  A  ther- 
moelectric pyrometer  consists  of  a  thermoelectric  couple  in  con- 
nection with  an  arrangement  for  indicating  the  electromotive 
force  between  the  hot  and  the  cold  junctions.  For  commercial 
purposes  a  millivoltmeter  of  suitable  sensitiveness  and  resistance 
is  a  satisfactory  indicator,  but  for  some  precise  work  a  potentiom- 
eter is  required. 

In  the  case  of  couples  found  useful  in  actual  measurements,  the 
relation  between  temperature  difference  and  electromotive  force 
through  a  considerable  temperature  range  can  be  expressed  by  a 
simple  equation.  For  couples  of  different  components,  different 
equations  are  required.  For  most  couples  used  in  commercial 
work,  one  or  the  other  of  the  following  equations  holds  with  a  fair 
degree  of  approximation  throughout  a  considerable  temperature 
range. 

E  =  a  +  U  +  ct2,  (27) 

log#  =  Alog*  +  £,  (28) 

where  E  is  the  electromotive  force  expressed  in  millivolts  for  a 
temperature  difference  of  t°  C.,  between  the  hot  and  cold  junction, 
while  a,  6,  c,  A,  and  B  are  constant  quantities  for  the  given  couple. 

The  purposes  of  this  experiment  are:  first,  to  construct  from 
experimentally  determined  data  a  curve  coordinating  the  tem- 
perature difference  and  the  electromotive  force  of  a  given  thermo- 
electric element;  and  secondly,  to  determine  the  departure  of  this 
empirical  curve  from  the  curves  expressed  by  (27)  and  (28). 

If  through  the  range  of  actual  measurement  the  empirical  curve 
can  be  represented  by  a  known  equation,  then  it  is  highly  probable 
that  the  curve  extended,  or  "  extrapolated,"  somewhat  beyond  the 
range  of  these  measurements  by  means  of  its  equation,  will  also 
represent  the  relation  between  the  two  variables  in  the  regions 
beyond  the  actual  measurements.  For  example,  if  a  certain 
equation  represents  the  relation  between  temperature  difference 
and  electromotive  force  of  a  given  thermoelectric  couple  from 
400°  to  800°  C.,  it  is  highly  probable  that  the  same  equation  will 


CALIBRATION  OF  A  THERMOELECTRIC  COUPLE         59 

represent  the  relation  between  these  quantities  from  300°  to  900°  C. 
This  furnishes  a  convenient  device  for  extending  a  curve  somewhat 
beyond  the  range  convenient  for  experimental  observations. 

For  this  experiment  several  definitely  known  and  easily  pro- 
duced temperatures  are  required.  These  conditions  are  most 
satisfactorily  met  by  the  melting  points  of  metallic  elements  and 
salts.  The  following  melting  points  are  convenient  for  the 
calibration  of  the  thermoelectric  pyrometers: 

Substances.  Melting  points,  °  C. 

Tin 232 

Bismuth 270 

Lead 327 

Zinc 419 

Antimony 630 

NaCl ,  800 

BaCl2 950 

Silver 961 

Copper 1083 

Nickel 1452 

The  temperature  at  which  a  substance  melts  is  that  at  which 
the  solid  and  liquid  states  remain  together  in  thermal  equilibrium. 
The  point  at  which  this  condition  obtains  can  be  inferred  as 
follows: 

With  one  junction  of  the  uncalibrated  thermoelectric  couple 
in  a  bath  maintained  at  constant  temperature,  and  the  other 
junction  in  a  mass  of  the  melted  substance,  observe  the  electro- 
motive force  as  the  substance  slowly  cools.  It  will  be  found  that 
as  the  substance  cools  the  electromotive  force  decreases;  that  after 
cooling  a  certain  amount  the  electromotive  force  remains  constant 
for  an  appreciable  interval  of  time;  that  during  this  interval  the 
substance  is  changing  from  the  liquid  to  the  solid  state;  and  that 
when  all  the  substance  has  solidified,  the  electromotive  force 
resumes  its  fall.  The  temperature  of  the  substance  during  the 
time-interval  of  constant  electromotive  force,  that  is,  of  constant 
temperature,  is  the  freezing  point  of  the  substance.  The  value 
of  the  freezing  point  is  obtained  from  tables.  Knowing  the 
freezing  points  of  a  number  of  substances,  together  with  the  corre- 


60  THERMOELECTRIC  PYROMETRY 

spending  electromotive  force  of  a  given  thermoelectric  couple,  a 
calibration  curve  for  the  given  couple  can  be  constructed  co- 
ordinating temperature  differences  and  potential  differences. 

To  locate  the  freezing  (or  melting)  point  of  a  substance,  the 
substance  is  melted;  the  supply  of  heat  is  turned  off;  and  while 
the  substance  is  cooling,  observations  of  the  electromotive  force 
of  the  thermoelectric  couple  being  tested  are  taken  every  half 
minute.  Make  a  cooling  curve  by  plotting  microvolts  as  ordi- 

nates  and  seconds  as  abscissas.  This 
curve  should  extend  from  a  temper- 
ature somewhat  above  the  freezing 
— 5550  point  to  a  temperature  somewhat 
below  the  freezing  point. 

Typical  cooling  curves  are  shown 
— 3450      in  Fig.  31.     From  these  curves  it  will 


.9??. 


^  be  observed  that  antimony  undercools 

and  then  rises  to  the  freezing  point. 

IGSO    \\Tith   the   particular   thermoelectric 

^^  couple  used,  the  electromotive  force 

*  in  Minute*  corresponding  to  the  freezing  point 

FlG  31  of  tin  is  1650  microvolts,  that  cor- 

responding to  the  freezing  point  of 

zinc  is  3450  microvolts  and  that  corresponding  to  the  freezing 
point  of  antimony  is  5550  microvolts.  The  temperatures  of  the 
freezing  substances  are  given  in  the  table  above. 

MANIPULATION.  —  In  the  manner  indicated,  find  the  electro- 
motive force  corresponding  to  the  freezing  point  of  five  substances, 
and  construct  a  curve  in  which  these  are  plotted  as  ordinates  and 
the  corresponding  freezing  points  are  plotted  as  abscissas.  This 
is  the  experimentally  determined  calibration  curve  of  the  given 
thermoelectric  pyrometer. 

In  case  the  indicator  of  the  pyrometer  is  divided  so  as  to  read 
temperatures  instead  of  microvolts,  the  ordinates  of  the  calibra- 
tion curve  would  represent  pyrometer  readings  instead  of  micro- 
volts. If  an  indicator  arranged  to  give  temperatures  is  correctly 
divided,  and  if  the  same  scale  is  used  to  plot  pyrometer  readings 


CALIBRATION  OF  A  THERMOELECTRIC  COUPLE         61 

and  freezing  points,  then  the  calibration  curve  will  be  a  straight 
line  equally  inclined  to  the  two  axes. 

In  the  calibration  of  a  thermoelectric  pyrometer,  the  couple 
should  be  protected  from  hot  gases  or  molten  substances  that 
would  alter  the  materials  of  which  it  is  composed.  The  couple 
should  be  immersed  in  the  molten  metals  to  about  the  same  depth 
it  is  to  be  immersed  in  future  use.  For  most  commercial  purposes 
an  immersion  of  20  6m.  will  be  sufficient.  The  calibrating  baths 
of  easily  oxidizible  metals  should  be  covered  by  a  layer  of  about 
2  cm.  of  powdered  carbon. 

If  the  empirical  calibration  curve  can  be  expressed  by  an  equa- 
tion having  the  form  of  (27)  or  (28)  then  it  can  be  extrapolated  to 
lower  and  also  to  higher  values  than  were  obtained  in  the  experi- 
ment. The  closeness  with  which  these  equations  represent  the 
curve  is  now  to  be  determined. 

For  example,  assume  for  the  moment  that  an  equation  of  the 
form  (27)  represents  the  empirical  calibration  curve.  The  validity 
of  this  assumption  will  now  be  tested.  Since  the  equation  contains 
three  independent  variables,  three  equations  will  be  required  for 
the  determination  of  their  values.  These  three  equations  can  be 
set  up  from  the  coordinates  of  any  three  points  of  the  curve. 
Thus,  representing  numerical  values  of  the  coordinates  of  any 
three  selected  points  by  the  symbols  (Ei}  h),  (E2,  22),  and  (#3),  we 
can  write: 

El  =  a  -f  bti  +  ctf, 
E2  =  a  +  bt2  +  ctf, 
#3  =  a  +  6*3  +  ctf. 

Since  the  empirical  curve  gives  the  actual  values  of  all  the 
quantities  in  these  equations  with  the  exception  of  the  three 
constants,  a,  6,  c,  the  values  of  these  constants  can  be  computed 
by  the  ordinary  method  for  solving  simultaneous  equations.  If 
the  empirical  curve  can  be  represented  by  an  equation  of  the  form 

E  =  a  +  bt  +  d2 
then  the  definite  equation  of  the  curve  traversing  the  three  selected 


62  THERMOELECTRIC  PYROMETRY 

points  will  be  obtained  by  substituting  for  the  constants  a,  6,  and 
c,  the  numerical  values  just  computed. 

Substitute  in  this  definite  equation  various  arbitrary  values  of 
t,  within  the  range  of  the  empirical  curve,  and  compute  the  corre- 
sponding values  of  E.  Plot  these  computed  points  on  the  sheet 
with  the  empirical  curve.  If  this  "computed  curve"  coincides 
with  the  empirical  curve,  then  the  definite  equation  above  obtained 
represents  the  empirical  curve  throughout  the  range  of  the  experi- 
ment. If  this  be  true,  the  empirical  curve  can  probably  be  extrap- 
olated to  a  limited  extent. 

In  case  it  is  found  that  the  empirical  curve  cannot  be  repre- 
sented by  an  equation  of  the  form  of  (27),  then  (28)  is  to  be  tested 
in  a  manner  analogous  to  that  just  described. 

Exp.  3.  The  Construction  and  Test  of  Thermoelectric  Couples 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  (14-19),  24.  If 
both  the  wires  composing  a  thermoelectric  couple  are  homogeneous, 
no  electromotive  force  will  be  developed  unless  the  two  junctions 
are  at  different  temperatures,  whatever  temperature  difference 
there  may  be  at  points  between  the  junctions.  But  if  in  either 
wire  there  be  inhomogeneity,  chemical  or  physical,  an  electro- 
motive force  will  be  developed  when  the  region  of  inhomogeneity 
is  at  a  temperature  different  from  that  of  the  remainder  of  the 
wire.  For  example,  an  unhomogeneous  alloy,  and  also  a  wire 
that  is  softer  at  one  place  than  at  another,  will  give  rise  to  para- 
sitic currents  when  ununiformly  heated.  Again,  some  substances 
undergo  allotropic  transformation  when  raised  to  certain  tem- 
peratures. For  example,  iron  heated  to  750°  C.  and  nickel 
heated  to  380°  C.  undergo  changes  that  persist  when  cooled  to 
ordinary  temperatures. 

For  these  reasons  wires  used  for  thermoelectric  couples  must 
be  chemically  and  physically  homogeneous  and  must  not  suffer 
allotropic  transformation  at  temperatures  within  the  range  for 
which  the  couple  is  to  be  used.  The  object  of  this  experiment  is 
to  construct  a  number  of  base  metal  thermoelectric  couples,  to 


CONSTRUCTION  AND  TEST  OF  THERMOELECTRIC  COUPLES  63 

test  them  for  homogeneity  and  freedom  from  allotropic  changes, 
and  to  calibrate  them  against  a  standardized  couple. 

MANIPULATION.  —  For  each  half  of  a  couple  use  a  wire  about 
one  meter  long  and  wrap  it  with  a  close  spiral  of  asbestos  string 
to  within  about  three  centimeters  of  each  end.  This  can  be  most 
conveniently  done  by  means  of  a  lathe  or  other  simple  rotating 
device.  Paint  the  asbestos  covering  with  a  paste  consisting  of 
100  parts  of  silica  flour,  50  parts  of  sodium  silicate  and  20  parts 
of  burnt  fire  clay.  Heat  the  wires  thus  prepared  in  a  tube  furnace 
till  the  paste  has  thoroughly  hardened.  Place  side  by  side  the  two 
wires  designed  to  constitute  one  couple  and  twist  one  pair  of  ends 
so  as  to  form  a  close  joint  one  to  two  centimeters  long. 

The  twisted  ends  may  be  fused  together  by  inserting  them 
in  the  flame  of  an  oxyhydrogen  or  an  oxyacetylene  blowpipe,  an 
electric  arc,  or  as  follows.  Connect  one  pole  of  a  110-volt  circuit 
to  the  untwisted  ends  of  the  couple,  and  connect  the  other  pole 
to  a  copper  or  carbon  rod  one  centimeter  or  more  in  diameter.  On 
causing  the  end  of  the  twisted  joint  to  approach  the  rod,  an  arc 
will  be  formed  which  will  fuse  together  the  ends  of  the  wires  of 
the  couple.  Under  no  circumstances  should  one  watch  the  fusing 
operation  with  unprotected  eyes.  One  should  either  use  smoked 
glass  goggles,  or  have  between  the  eyes  and  the  work  a  screen  of 
smoked  glass  or  one  consisting  of  blue  and  red  glass. 

The  thermoelectric  couple  is  now  ready  to  be  tested  and  cali- 
brated. To  test  a  couple  for  homogeneity,  connect  the  terminals 
to  a  galvanometer,  immerse  the  junctions  in  a  water  or  ice  bath, 
and  slowly  pass  the  flame  of  a  Bunsen  burner  along  the  length  of 
the  couple.  If  no  change  of  deflection  is  produced,  the  wires  of 
the  couple  are  homogeneous. 

To  calibrate  a  number  of  couples,  all  of  the  hot  junctions, 
together  with  the  hot  junction  of  a  standardized  couple,  are  placed 
in  the  middle  of  a  tube  furnace.  The  cold  junction  of  the  stand- 
ard couple  is  maintained  at  the  temperature  at  which  it  was  cali- 
brated, and  the  temperature  of  the  cold  junctions  of  the  other 
couples  is  to  be  maintained  at  a  temperature  as  nearly  constant 
as  possible.  For  this  purpose  may  be  used  a  bath  of  melting  ice. 


64 


THERMOELECTRIC  PYROMETRY 


Couples  ketitg  Cali.bj-.aied 

FIG.  32. 


Readings  of  the  electromotive  force  generated  by  each  couple 
are  now  to  be  taken  for  a  series  of  furnace  temperatures.  As  com- 
mercial base  metal  couples  have  higher  electromotive  forces  than 
a  platinorhodium  couple,  it  will  be  necessary  to  use  a  higher 
resistance  in  series  with  the  base  metal  couples  than  that  in  series 
with  the  standard  couple.  For  this  experiment  a  millivoltmeter 
and  switches  arranged  as  in  Fig.  32  will  be  convenient.  In  this 

diagram,  C  is  the  moving  coil  of  a 
sensitive  millivoltmeter,  A,  B  are 
the  terminals  of  the  low  resistance 
coil  of  the  millivoltmeter  and  A,  D 
are  the  terminals  of  the  high  re- 
sistance coil.  Some  instruments  are 
provided  with  a  device  by  means 
of  which  the  pointer  can  be  clamped 
while  the  instrument  is  being  moved. 
To  release  the  pointer  the  milled 

head  is  rotated  till  the  pointer  swings  freely.  On  closing  the 
switch  S,  connected  to  the  standard  couple,  the  electromotive 
force  generated  by  this  couple  will  be  impressed  on  the  milli- 
voltmeter. On  opening  this  switch  and  closing  the  switch  K\t 
connected  to  the  first  base  metal  couple,  the  electromotive  force 
generated  by  this  couple  will  be  indicated  on  the  millivoltmeter. 
Thus  the  electromotive  force  generated  by  any  one  of  the  couples 
can  be  measured. 

In  order  that  during  the  time  an  observation  is  being  taken  the 
temperature  of  the  furnace  may  be  fairly  constant,  it  will  be 
necessary  to  open  the  furnace  switch  a  couple  of  minutes  before 
observations  are  taken.  Proceed  as  follows:  When  the  furnace 
is  at  about  200°,  open  the  furnace  switch,  wait  till  the  temperature 
becomes  constant,  and  then  in  quick  succession  take  millivoltmeter 
readings  with  the  standard  couple,  couple  No.  1,  the  standard, 
couple  No.  2,  the  standard,  couple  No.  3,  etc.  Note  the  tem- 
peratures of  the  cold  junctions  of  the  base  metal  couples  as 
indicated  by  a  mercury-in-glass  thermometer.  Close  the  switch, 
wait  till  the  temperature  is  about  300°  C.,  and  then  in  quick 


CONSTRUCTION  AND  TEST  OF  THERMOELECTRIC  COUPLES  65 


succession  take  readings  with  the  standard  couple,  couple  No.  1, 
the  standard,  couple  No.  2,  the  standard,  as  before.  Note  the 
temperature  of  the  cold  junction  of  the  base  metal  couples.  Con- 
tinue at  50°  intervals  throughout  the  range  required.  While  the 
furnace  cools,  take  readings  at  50°  intervals. 
Tabulate  the  observed  data  as  follows: 

COLD  JUNCTIONS  AT  0°  C. 


Standard 
millivolts. 

Couple  No.  1 
millivolts. 

Standard 
millivolts. 

Couple  No.  2 
millivolts. 

Standard 
millivolts. 

Couple  No.  3 
millivolts. 

Standard 
millivolts. 

Find  the  mean  of  the  two  electromotive  forces  developed  by 
the  standard  couple  before  and  after  each  reading  of  the  base  metal 
couples.  From  a  previously  determined  calibration  curve  of  the 
standard  couple  find  the  temperature  corresponding  to  each  of 
these  means.  Take  these  values  as  the  furnace  temperatures  at 
the  time  the  various  base  metal  couple  readings  were  made. 

Tabulate  the  furnace  temperatures  and  the  electromotive  forces 
of  the  various  base  metal  couples.  With  furnace  temperatures  as 
abscissas  and  electromotive  forces  as  ordinates,  construct  on  one 
pair  of  coordinate  axes  a  calibration  curve  for  each  base  metal 
couple. 

By  means  of  the  method  described  in  the  preceding  experiment, 
find  the  equation  of  some  one  of  these  calibration  curves.  From 
this  equation  compute  the  electromotive  forces  corresponding  to 
a  series  of  assumed  hot-junction  temperatures.  On  a  second  sheet 
of  cross-section  paper  construct  the  computed  curve  and  also  the 
empirical  curve  on  which  it  is  based. 


66  THERMOELECTRIC  PYROMETRY 

Exp.  4.  Determination  of  Temperature  by  Means  of  a  Thermo- 
electric Pyrometer  with  the  Cold  Junction  not  Maintained 
at  a  Constant  Temperature 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  (24,  25).  It  often 
happens  that  a  thermoelectric  couple  calibrated  with  the  cold 
junction  at  a  known  constant  temperature  is  afterward  used  under 
conditions  in  which  the  cold  junction  cannot  be  maintained  at  a 
constant  temperature.  If  the  equation  of  the  calibration  curve 
of  the  thermoelectric  couple  is  known  at  any  definite  cold-junction 
temperature,  the  correction  to  be  applied  to  the  indicated  tempera- 
ture when  the  cold  junction  is  at  any  definite  temperature  can  be 
determined  by  the  method  described  in  Arts.  25  and  26.  The 
object  of  this  experiment  is  to  obtain  a  series  of  temperature 
observations  from  a  calibrated  thermoelectric  pyrometer  when  the 
temperature  of  the  cold  junction  is  known  but  variable,  and  then 
to  determine  the  actual  temperatures  corresponding  to  the  ob- 
served values. 

MANIPULATION.  —  Insert  in  an  electric  tube  furnace  the  hot 
junction  of  a  couple  in  connection  with  a  direct-reading  indicator 
and  also  the  hot  junction  of  a  standard  couple.  The  cold  junction 
of  the  standard  couple  is  to  be  maintained  at  0°  C.  by  means  of  a 
bath  of  melting  ice.  No  attempt  is  to  be  made  to  maintain 
constant  the  temperature  of  the  cold  junction  of  the  test  couple, 
but  its  temperature  is  to  be  obtained  by  means  of  a  mercury-in- 
glass  thermometer. 

At  about  200°  C.  note  in  quick  succession,  the  millivolts 
produced  by  the  standard  couple,  the  reading  of  the  instrument 
connected  to  the  test  couple,  the  millivolts  produced  by  the 
standard  couple  and  the  temperature  of  the  cold  junction  of  the 
test  couple.  Take  similar  observations  at  100°  intervals  through- 
out the  range  of  the  test  couple.  In  this  experiment  all  electro- 
motive forces  are  to  be  measured  by  means  of  a  potentiometer, 
Arts.  20  and  21. 

By  the  method  described  in  Arts.  24  and  25,  compute  the  tem- 
perature corresponding  to  the  indicated  temperature  of  the  test 


SPECIMEN  OF  STEEL  67 

couple.     From  the  calibration  curve  of  the  standard  couple  note 
the  actual  temperatures. 

All  the  data,  observed  and  computed,  should  be  arranged 
systematically  in  a  table.  In  the  column  next  to  the  last  put  the 
computed  temperatures,  and  in  the  last  column  put  the  tempera- 
tures obtained  from  the  standard  couple. 

Exp.    5.   Determination    of   the    Transformation   Points    of   a 
Specimen  of  Steel 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  (14-19).  Many 
substances  undergo  a  transformation  into  a  different  condition 
when  they  are  subjected  to  a  certain  temperature.  Such  a  trans- 
formation is  accompanied  either  by  an  evolution  or  an  absorption 
of  heat.  The  temperatures  at  which  these  transformations  occur 
are  called  " transformation  points"  or  " critical  points."  Some 
substances  have  several  transformation  points.  Transformation 
points  are  observed  in  the  case  of  metals  that  have  different  allo- 
tropic  forms,  alloys,  salts  that  have  different  amounts  of  water  of 
crystallization,  and  solutions  that  have  different  amounts  of  water 
of  hydration.  When  iron  or  steel  passes  through  certain  of  its 
transformation  points  the  hardness,  coarseness  of  grain,  and 
magnetic  properties  are  considerably  altered.  The  properties  of 
steel  acquired  at  any  temperature  can  be  made  permanent  by 
sudden  quenching.  The  temperature  at  which  a  given  specimen 
of  steel  may  be  quenched  in  order  that  the  required  properties 
may  be  fixed  is  determined  by  the  transformation  points  of  the 
specimen.  In  the  heat  treatment  of  steel  the  most  important 
transformation  point  is  that  at  which  the  grain  is  the  finest  and 
is  the  point  at  which  the  specimen  should  be  quenched  in  order 
that  the  hardness  may  be  a  maximum.  This  temperature  is 
called  the  "decalescent  point." 

If  heat  be  gradually  added  to  a  specimen  of  steel  all  of  the  energy 
absorbed  will  be  used  in  raising  the  temperature  of  the  specimen, 
until  the  temperature  is  about  650°  C.  At  this  point  some  of  the 
energy  absorbed  will  be  used  in  producing  internal  molecular 
changes.  This  transformation  point  is  known  as  the  "Ac2  point." 


68  THERMOELECTRIC  PYROMETRY 

When  the  specimen  acquires  a  temperature  in  the  neighborhood 
of  745°  C.,  all  of  the  energy  absorbed  at  that  temperature  will  be 
used  in  producing  internal  changes.  This  transformation  is 
exhibited  by  a  sudden  cessation  of  the  rise  in  temperature  of  the 
specimen.  This  transformation  point  is  known  as  the  "Aci 
point,"  or  the  "decalescent  point."  The  Aci  transformation  is 
completed  within  a  temperature  range  of  a  few  degrees,  but  the 
Acz  transformation  takes  place  throughout  the  range  from  about 
650°  C.  to  about  765°  C.  A  third  transformation  called  the 
"Ac3  transformation,"  takes  place  from  about  780°  C.  to  about 
810°  C. 

On  cooling  the  specimen,  a  series  of  reverse  changes  take  place 
but  at  different  temperatures.  These  transformations  are  accom- 
panied by  an  evolution  of  heat  which  is  exhibited  by  increases  in 
temperature.  The  transformation  point  of  the  cooling  specimen 
analogous  to  the  decalescent  point  is  called  the  "Ari  point"  or  the 
"recalescent  point." 

The  object  of  this  experiment  is  to  determine  the  transformation 
points  of  a  specimen  of  steel. 

MANIPULATION.  —  On  very  slowly  heating  a  specimen  of  steel 
there  is  such  a  sudden  interruption  in  the  rise  of  temperature  at 
the  decalescent  point,  and  on  very  slowly  cooling  the  specimen 
there  is  such  a  sudden  interruption  in  the  fall  of  temperature  at 
the  recalescent  point,  that  those  two  points  can  be  readily  observed 
by  an  ordinary  thermoelectric  pyrometer.  To  locate  the  other 
transformation  points  a  more  sensitive  method  is  required.  A 
method  that  can  be  applied  to  the  location  of  all  the  transformation 
points  will  now  be  described. 

The  specimen  of  steel  and  a  piece  of  some  metal  such  as  nickel 
that  does  not  exhibit  transformation  points  within  the  range  of 
transformation  points  of  steel  are  placed  together  within  an 
electrically  heated  furnace.  The  terminals  of  a  rhodioplatinum 
couple  AC,  Fig.  33,  are  joined  to  a  milli voltmeter  V.  This 
thermoelectric  pyrometer  indicates  the  temperature  of  the  steel 
specimen.  A  second  couple  BDG  consists  of  a  short  length  of 
rhodioplatinum  alloy  BD  joined  to  two  lengths  of  pure  platinum 


SPECIMEN  OF  STEEL 


69 


wire.  The  junctions  A  and  B  are  at  the  temperature  of  the  steel 
specimen,  and  the  junction  D  is  at  the  temperature  of  an  adjacent 
piece  of  nickel. 


FIG.  33. 

So  long  as  the  steel  and  the  nickel  are  at  the  same  temperature, 
the  sensitive  galvanometer  G  will  be  undeflected.  But  when  a 
molecular  transformation  of  the  steel  occurs,  there  will  be  either 
an  evolution  or  absorption  of  heat  by  the  specimen,  and  the 
galvanometer  G  will  be  deflected.  In  this  arrangement,  the 
galvanometer  G  serves  as  a  sensitive  indicator  of  the  presence  or 


FIG.  34. 

absence  of  molecular  transformation,  while  the  millivoltmeter  V 
serves  to  indicate  the  temperature  of  the  specimen. 

The  first  time  the  apparatus  is  used,  it  will  be  necessary  to  run 
a  preliminary  experiment  in  order  to  determine  the  setting  of 
the  furnace  rheostat  to  give  the  proper  rate  of  heating,  and  in 
order  that  the  resistance  in  series  with  the  galvanometer  may 


70 


THERMOELECTRIC  PYROMETRY 


have  the  value  that  will  give  the  galvanometer  the  maximum 
sensitiveness  consistent  with  the  requirement  that  at  no  time  shall 
the  deflection  be  beyond  the  limits  of  the  scale.  Place  the  sample, 
properly  connected  to  the  two  thermoelectric  couples,  within  the 
furnace  and  adjust  the  furnace  rheostat  till  the  temperature  will 
rise  to  about  800°  C.  in  45  minutes.  Put  sufficient  resistance  in 

series  with  the  galvanometer  that 
the  deflection  produced  at  the 
decalescent  point  will  remain  on 
the  scale. 

In  performing  an  experiment, 
connect  up  the  apparatus,  place 
the  cold  junction  C  in  a  bath  of 
melting  ice,  set  the  furnace  rheostat 
at  the  predetermined  position,  close 
the  furnace  switch,  and  when  the 
temperature  of  the  specimen  has 
reached  about  600°  C.,  start  tak- 
ing simultaneous  readings  of  the 
millivoltmeter  and  galvanometer. 
These  readings  should  be  taken  at 
10°  C.  intervals  to  a  temperature 
thirty  or  more  degrees  above  the 
decalescent  point.  Then  open  the 
furnace  switch  and  continue  tak- 
ing simultaneous  readings  at  10°  C.  intervals  while  the  specimen 
cools  to  about  600°  C.  After  having  started  to  take  readings 
do  not  alter  the  setting  of  the  furnace  rheostat. 

With  temperatures  as  ordinates  and  galvanometer  deflections 
as  abscissas,  plot  a  heating  curve  and  a  cooling  curve  of  the 
specimen.  A  typical  pair  of  curves  is  shown  in  Fig.  35.  From 
an  inspection  of  this  curve  point  out  the  various  transformation 
points  and  the  ranges  through  which  the  transformations  extend. 


10  0  10 

FIG.  35. 


CHAPTER  IV 
RADIATION   PYROMETRY 

29.   The  Experimental  Realization  of  Black-body  Radiation.  — 

Though  no  known  substance  fulfills  the  definition  of  black-body, 
Kirchhoff  has  shown  that  black-body  radiation  can  be  experi- 
mentally realized.     Let  A,  Fig.  36,  represent  an  ideal  black-body 
within  a  uniformly  heated  athermanous 
enclosure,  and  in  thermal  equilibrium  with 
it.     Being  in   thermal  equilibrium  with 
its  surroundings  it  radiates  to  the  walls 


•# 


of   the    inclosure    the    same   amount  of  JTIG  35 

energy  it  receives  from  them.     Since  it 

radiates  to  the  wall  behind  it  the  same  amount  of  energy  it  re- 
ceives from  that  wall,  to  an  observer  at  0,  the  body  and  the 
background  are  equally  bright.  Therefore,  the  walls  of  a 
uniformly  heated  athermanous  enclosure  radiate  as  an  ideal 
black-body.  If  a  small  aperture  be  made  in  the  enclosing  wall, 
the  radiance  that  will  emerge  from  the  enclosure  will  be  that  of  a 
black-body. 

In  the  succeeding  pages  a  uniformly  heated  athermanous  en- 
closure will  be  called  a  " black-body"  with  quotation  marks.  The 
production  of  black-body  radiance  from  the  interior  of  a  heated 
enclosure  requires  (a)  that  the  temperature  of  the  enclosure  be 
uniform  throughout,  (6)  that  the  walls  of  the  body  be  atherma- 
nous, (c)  that  all  frequencies  of  black-body  radiance  be  present, 
(d)  that  all  radiance  be  due  to  temperature  —  no  luminescence 
effects. 

It  can  thus  be  shown  that  any  body  within  a  uniformly  heated 
enclosure  and  in  thermal  equilibrium  with  its  surroundings, 
radiates  like  a  black-body.  Suppose  the  same  enclosure  contains 

71 


72 


RADIATION  PYROMETRY 


|s 

=1=1= 

a 

=^0 

a  body  Bf  Fig.  36,  which  has  a  transmitting  factor  and  an  absorp- 
tive factor  of  any  value.  Since  the  body  is  assumed  to  remain  in 
thermal  equilibrium  .with  its  surroundings,  it  is  receiving  energy 
from  all  directions  and  is  emitting  energy  in  all  directions  at  the 
same  rate.  An  observer  at  0,  will  receive  energy  at  the  same  rate 
from  elements  'of  area  of  the  body  and  from  elements  of  the  en- 
closing walls.  Consequently,  the  surface  of  the  body  radiates  like 
a  black-body.  A  black-body  is  sometimes  called  a  "complete 
radiator"  or  " integral  radiator." 

The  bore  of  an  uniformly  heated  tube,  long  compared  with  its 
diameter,  emits  radiance  that  is  essentially  the  same  as  that  from 
an  ideal  black-body.  As  nearly  uniform  temperatures  as  may  be 
desired  can  be  secured  by  electric  heating.  Two  methods  of 
electric  heating  are  in  vogue.  The  first  consists  in  the  use  of  an 

electric  current  in  a  spiral 
conductor  of  high  resistance 
and  high  melting  point 
wrapped  closely  about  the 
tube  to  be  heated,  Fig.  37. 
The  temperature  is  regulated  by  varying  the  resistance  in  circuit 
with  the  heating  coil.  For  temperatures  up  to  1100°  C.  the 
alloy  called  "nichrome  II,"  is  available;  for  temperatures  up  to 
1500°  C.,  platinum  can  be  used.  The  temperature  of  the  ends 
of  the  tube  may  be  kept  at  the  _ 
same  as  that  of  the  middle  by 
having  about  the  ends  of  the  tube 
more  turns  of  conductor  per  unit 
length  of  the  tube,  than  about 
the  middle.  In  case  the  ends  are 
at  a  different  temperature  than 
the  middle  of  the  tube,  the  de- 
parture from  black-body  radiation  can  be  diminished  by  the  use 
of  perforated  diaphragms  placed  inside  the  tube  near  the  ends. 

The  uniformity  of  temperature  along  the  axis  of  the  tube  can  be 
tested  by  means  of  a  thermoelectric  pyrometer.  An  electric 
furnace  that  is  more  robust  under  protracted  use  at  high  tempera- 


FIG.  37. 


FIG.  38. 


THE  GENERAL  PRINCIPLES  OF  RADIATION  PYROMETRY    73 

tures  consists  of  a  refractory  tube  on  which  is  strung  a  column  of 
thin  graphite  discs,  Fig.  38.  The  end  discs  are  joined  to  the  low 
potential  terminals  of  a  step-down  transformer  connected  in  series 
with  an  ammeter.  By  altering  the  pressure  between  the  graphite 
discs  by  means  of  a  pair  of  hand  screws,  the  electric  resistance  of 
the  graphite  column  can  be  altered,  and  thereby  the  temperature 
of  the  axial  tube. 

For  use  as  a  "  black-body,"  a  current-carrying  carbon  furnace 
has  one  point  of  inferiority  as  compared  with  a  current-carrying 
wire  furnace  in  the  great  difficulty  in  maintaining  a  constant 
temperature.  This  is  due  to  the  fact  that  the  resistance  of  carbon 
diminishes  with  an  increase  of  temperature,  whereas  the  resistance 
of  the  metals  used  in  furnaces  increases  with  an  increase  of  tem- 
perature. With  a  metal-wound  furnace,  the  temperature  can  be 
maintained  at  a  nearly  fixed  value  by  adjusting  the  resistance  in 
circuit  till  the  current  is  such  that  the  heat  produced  in  the  furnace 
equals  the  heat  dissipated  by  radiation,  conduction,  and  convec- 
tion. With  a  carbon  furnace,  if  the  resistance  in  circuit  be  in- 
creased, the  lower  current  will  also  be  accompanied  by  a  decrease 
in  temperature.  But  this  decrease  in  temperature  by  causing  an 
increase  in  the  resistance  of  the  carbon  will  cause  a  further  de- 
crease of  current,  and  this,  in  time,  a  further  decrease  of  tempera- 
ture. This  action  will  then  be  repeated. 

30.  The  General  Principles  of  Radiation  Pyrometry.  —  The 
fact  that  the  rate  with  which  a  black-body  radiates  energy  is  a 
function  of  the  thermodynamic  temperature  (Art.  7),  is  the  basis 
of  a  valuable  system  of  high  temperature  measurement  called 
"  Radiation  Pyrometry."  In  this  system,  radiance  of  all  fre- 
quencies emitted  by  the  source  is  allowed  to  impinge  on  a  distant 
absorbing  body  of  small  size  and  thermal  capacity.  The  rise  in 
temperature  of  the  absorbing  body  is  a  measure  of  the  rate  with 
which  energy  is  incident  upon  it,  and  this  of  the  temperature  of 
the  source. 

In  the  radiation  pyrometers  now  in  successful  use,  radiance  is 
concentrated  by  means  of  a  collective  lens  or  mirror  upon  a  small 
and  sensitive  temperature  measuring  device  such  as  a  thermo- 


74  RADIATION  PYROMETRY 

junction  in  connection  with  a  milli voltmeter.  Radiance  of  all 
frequencies,  visible  and  invisible,  incident  on  a  lampblack-coated 
junction  of  such  a  thermoelectric  element  will  be  almost  entirely 
absorbed  and  transformed  into  heat.  This  heat  will  raise  the 
temperature  of  the  receiving  junction  by  an  amount  proportional 
to  the  energy  absorbed,  thereby  producing  an  electromotive  force 
of  a  value  depending  upon  the  difference  in  temperature  of  the  two 
junctions  of  the  element.  Thus,  if  the  fraction  of  the  total  inci- 
dent energy  absorbed  by  the  receiving  surface  were  constant,  the 
indications  of  the  millivoltmeter  would  show  the  rate  with  which 
energy  is  radiated  by  the  source. 

It  is  found  that  the  fraction  of  the  total  incident  energy  that 
is  absorbed  by  the  receiving  surface  is  not  a  constant  fraction  for 
all  temperatures,  but  that  it  is  a  function  of  the  temperature  of  the 
radiating  source.  In  fact,  experiment  shows  that  when  a  lamp- 
blacked  thermoelement  is  exposed  to  radiance  from  a  black-body 
at  thermodynamic  temperature  T,  there  is  developed  an  electro- 
motive force  E  of  the  value 

E  =  aTb,  (29) 

where  a  and  b  are  constants  for  any  particular  instrument.  These 
constants  can  be  found  from  the  observation  of  the  electromotive 
forces  developed  when  the  instrument  is  exposed  to  the  radiance 
from  a  black-body  at  two  known  temperatures. 

After  these  constants  are  determined,  the  above  equation  can 
be  employed  to  determine  the  thermodynamic  temperature  of  any 
substance  that  radiates  like  a  black-body.  But  the  application 
of  this  method  to  a  substance  that  does  not  radiate  like  a  black- 
body  would  not  give  thermodynamic  temperatures.  For  example, 
if  a  piece  of  black  carbon,  one  of  polished  platinum,  and  one  of 
transparent  glass  be  placed  within  a  "black-body,"  as  in  Fig.  36, 
then  after  the  system  has  attained  thermal  equilibrium  all  three 
bodies  are  at  the  same  thermodynamic  temperature.  And  since 
all  three  bodies  are  radiating  at  the  same  rate,  they  are  at  a  com- 
mon black-body  temperature.  If  the  three  specimens  be  quickly 
removed  from  the  enclosure  they  will  radiate  at  quite  different 


THE  FERY  THERMOELECTRIC  PYROMETER 


75 


rates.  The  carbon  will  radiate  about  as  before,  the  platinum  at 
a  much  less  rate,  and  the  glass  will  radiate  scarcely  at  all.  That  is, 
though  all  three  bodies  are  at  the  same  thermodynamic  tempera- 
ture, they  are  now  at  quite  different  black-body  temperatures.  A 
radiometer  actually  indicates  black-body  temperatures.  But 
when  the  body  being  studied  radiates  as  a  black-body,  its  black- 
body  temperature  equals  its  thermodynamic  temperature. 

31.   The  Fery  Thermoelectric  Mirror  Radiation  Pyrometer.  - 
This  instrument  consists  of  a  concave  gold-plated    mirror   M, 
Fig.  39,  and  a  small  thermoelectric  couple  T,  connected  to  a  milli- 
voltmeter  by  means  of  binding 
posts  BBr.     By  means  of  a 
rack  and  pinion  P,  the  concave 
mirror  can  be  moved  till  the 
image  of  the  source  is  on  one 
junction  of  the  thermocouple. 

This  focalizing  is  facilitated 
by  an  eyepiece  E,  in  front  of 
an  aperture  in  the  concave 
mirror,  together  with  two 
semicircular  plane  mirrors  m 
mounted  in  the  thermocouple  FlG  39 

box.     A  semicircular  notch  in 

the  middle  of  the  straight  side  of  each  plane  mirror  permits 
the  passage  of  radiance  reflected  from  the  concave  mirror  to  reach 
the  thermoj  unction.  These  semicircular  plane  mirrors  are  in- 


FIG.  40.        FIG.  41. 


FIG.  42. 


clined  to  one  another  at  an  angle  of  about  5°,  Fig.  40.     When  the 
aperture  in  the  semicircular  mirrors  coincides  with  the  image  of 
the  source  sighted  upon,  the  field  of  view  is  a  circle  with  a  dark 
X 


76 


RADIATION  PYROMETRY 


center,  Fig.  41.  When  the  image  is  either  in  front  of  or  behind 
this  aperture,  the  field  of  view  consists  of  two  semicircles  displaced 
relative  to  one  another,  Fig.  42.  In  Fig.  43  the  Fery  Thermoelec- 
tric Mirror  Pyrometer  E  is  shown  in  connection  with  the  milli- 
voltmeter  G. 


FIG.  43. 


It  will  now  be  shown  that  to  a  close  degree  of  approximation, 
the  rate  with  which  radiance  is  received  by  the  thermo junction  of 
a  Fery  Thermoelectric  Pyrometer  is  independent  of  the  distance 
of  the  focalized  instrument  from  the  source. 


FIG.  44. 

Let  J  represent  the  rate  of  incidence  of  radiance  on  the  thermo- 
couple; /  the  rate  with  which  energy  is  emitted  from  unit  area  of 
the  source;  A0,  the  area  of  the  part  of  the  source  from  which 
radiance  reaches  the  thermocouple;  Ai}  the  area  of  the  image  of 


THE  F£RY  THERMOELECTRIC  PYROMETER      77 

AO,*  u,  the  distance  from  the  source  to  the  mirror;  v,  the  distance 
from  the  image  to  the  mirror. 

Now  the  total  radiance  incident  on  the  thermocouple  is  pro- 
portional :  (a)  to  the  rate  with  which  energy  is  emitted  from  unit 
area  of  the  source;  (&)  to  the  area  of  the  part  of  the  source  from 
which  radiance  reaches  the  thermocouple;  (c)  inversely  propor- 
tional to  u2',  (d)  proportional  to  the  aperture  of  the  mirror.  That 
is 


u2 
But  from  a  property  of  spherical  mirrors, 

AQ  _  U? 

Consequently, 

[T    A      7  oT                T    A              O7*>  T    jl      7  O 

iAo/i         lAtiF  n*      lAihz      T  . 
oc— —    oc — i -<x^-oc/A,.tan20, 
w2    J          z;2      w2          z;2 

or, 

j-  <x/tan20. 

In  the  Fery  Mirror  Radiation  Pyrometer,  0  is  maintained  con- 
stant by  means  of  a  system  of  diaphragms  in  the  thermocouple 
box.  Therefore,  the  above  variation  reduces  to 

j-oc/.  (30) 

That  is,  under  the  conditions  expressed  and  assumed  in  the 
above  discussion,  the  rate  with  which  radiance  is  incident  on  the 
thermoc6uple  of  the  Fery  Mirror  Thermoelectric  Radiation 
Pyrometer  is  proportional  to  the  intensity  of  the  radiating  source 
and  is  independent  of  the  distance  between  the  source  and  the 
focalized  instrument.  In  this  discussion  it  has  been  assumed :  (a) 
that  the  image  of  the  source  is  not  smaller  than  the  absorbing 
surface;  (6)  that  the  angle  6,  Fig.  44,  remains  constant.  The 
dimensions  of  the  industrial  form  of  the  instrument  are  such  that 
these  two  conditions  are  realized  to  a  close  degree  of  approximation 
when  the  distance  from  the  source  to  the  focalized  instrument 


78      9  RADIATION  PYROMETRY 

exceeds  one  meter,  and  when  at  the  same  time  the  radiating  source 
is  so  large  that  its  image  covers  the  disc  soldered  on  the  ends  of 
the  thermocouple. 

The  relation  between  the  radius  r  of  the  source  and  the  distance 
I  from  the  source  to  the  thermocouple,  Fig.  44,  is 

tan0  =  -y 

i 

in  which  6  is  a  constant  for  any  particular  instrument  determined 
by  the  focal  length  of  the  converging  mirror  and  the  aperture  of 
the  thermocouple  box. 

For  sources  of  small  temperature,  the  instrument  is  used  with 
the  receiving  end  entirely  open.  But  if  the  aperture  A  A'  were 
entirely  open  when  sighted  on  sources  of  high  temperature,  the 
millivoltmeter  might  be  deflected  beyond  the  end  of  the  scale  and 
the  thermoelectric  junction  might  even  be  injured  by  the  high 
temperature  of  the  image.  To  guard  against  these  dangers,  when 
employed  to  measure  high  temperatures,  the  aperture  is  partially 
closed  by  a  sectored  diaphragm,  Fig.  52,  which  cuts  off  a  definite 
fraction  of  the  incident  radiance. 

The  millivoltmeter  can  be  divided  so  as  to  indicate  tempera- 
tures directly.  Two  scales  are  usually  provided,  one  for  use  when 
the  receiving  end  is  open,  and  another  for  use  when  partially 
closed  by  the  sectored  diaphragm.  Commercial  instruments  of 
the  Fery  Mirror  type  are  constructed  with  a  range  from  600°  to 
1500°  C.  and  over. 

Usually  the  principal  focal  length  of  the  concave  mirror  is  7.6 
cm.,  and  the  diameter  of  the  aperture  of  the  diaphragm  of  the 
thermoelectric  couple  box  is  0.15  cm.  For  an  instrument  having 
these  constants  the  following  table  gives  the  diameter  of  source 
required  for  various  distances  of  I  between  source  and  receiver. 


^-ter  of  source,  en, 

80  ...................  1.4 

100  ...................  1.8 

150  ...................  3.1 

200  ...................  4.2 

300  ...................  6.3 

500..  10.7 


THE  FERY  SPIRAL  PYROMETER 


79 


32.  The  Relation  between  the  Energy  Rate  at  a  Point  and  the 
Distance  from  the  Source.  —  The  radiance  incident  at  a  point  is 
directly  proportional  to  the  effective 
area  of  the  radiating  surface  and  in- 
versely proportional  to  the  square  of 
the  distance  between  the  emitting 
surface  and  the  receiving  body.  Thus 
if  a  diaphragm  D,  Fig.  45,  be  placed 
in  front  of  a  radiating  surface  S,  then 
with  respect  to  a  point  0,  at  a  dis- 
tance I,  the  area  of  the  radiating 

surface  is  A.    Whence  the  energy  per  unit  tune,  J,  incident  on  0, 
is  expressed  by  the  equation 

A 


FIG.  45. 


where  k  is  a  coefficient  of  proportionality.     If  the  distance  I  be 

large  compared  with  the  diameter  of  the  effective  area  A,  then  — 

i 

measures  the  solid  angle  subtended  at  0,  by  the  surface  sending 
energy  to  0.     Representing  this  solid  angle  by  the  symbol  o> 

J  =  k'o. 

That  is,  so  long  as  the  solid  angle  subtended  by  the  source  at  the 
receiving  point  is  constant,  the  rate  with  which  radi- 
ance is  incident  at  the  receiving  point  is  independent 
of  the  distance  between  the  source  and  the  receiving 
body. 

33.  The  Fery  Spiral  Pyrometer. — This  instrument 
is  the  same  as  Fery's  Thermoelectric  Mirror  Pyrom- 
eter except  that  in  place  of  the  incident  radiance  being 
reflected  to  one  junction  of  a  thermoelectric  couple, 
the  incident  radiance  is  reflected  to  a  small  blackened 
spiral,  Fig.  46,  which  will  coil  or  uncoil  as  the  temperature  of 
the  spiral  is  increased  or  decreased.  This  sensitive  spiral  consists 
of  a  double  ribbon  of  two  metals  of  different  thermal  expansion 
coefficients.  The  two  ribbons  being  fastened  together  throughout 


FIG.  46. 


80 


RADIATION  PYROMETRY 


their  length,  an  increase  in  temperature,  by  causing  one  of  the 
ribbons  to  expand  more  than  the  other,  will  result  in  the  spiral 
coiling  up  more  closely.     The  end  of  the  double  strip  at  the  center 
of  the  spiral  is  attached  to  a  shank  on  which 
is  mounted  a  pointer  that  moves  over  a 
circular  scale  as  the  spiral  coils  or  uncoils. 
This  scale  is  empirically  graduated  to  indi- 
cate temperatures. 

When  the  instrument  is  placed  in  front  of 
a  hot  body  the  spiral  will  be  quickly  heated 
and  the  whole  case  will  be  slowly  raised  in 
temperature.  There  will  thus  be  produced 
a  slow  creep  of  the  pointer  superposed  on  a 
sudden  deflection.  In  using  the  instrument, 
the  reading  should  not  be  taken  till  the 
slow  creep  has  ceased.  As  the  Fery  Spiral 
Pyrometer  requires  no  millivoltmeter  or  other 
accessory  apparatus  it  is  much  more  portable 
than  the  Thermoelectric  Mirror  Pyrometer. 
34.  Fixed  Focus  Radiation  Pyrometers.  —  Any  radiation  or 
optical  pyrometer  should  give  the  same  indication  when  the 
distance  from  the  source  is  altered  through  considerable  limits. 
This  requirement  will  be  met  if  the  cone  of  light  incident  on  the 
receiving  device  is  of  a  constant  solid  angle.  The  constancy  of 
this  solid  angle  can  be  maintained:  (a)  by  a  diaphragm  in  com- 
bination with  a  concave  spherical  mirror  focalized  on  the  source 
as  in  the  F&y  Thermoelectric  Mirror  Radiation  Pyrometer  (Art. 
31);  (6)  by  a  diaphragm  in  combination  with  a  converging  lens 
focalized  on  the  source  (Art.  42) ;  (c)  by  a  diaphragm  in  combina- 
tion with  a  converging  spherical  lens  or  mirror  focalized  on  the 
aperture  of  the  diaphragm,  Fig.  48;  (d)  by  a  diaphragm  in  com- 
bination with  a  conical  mirror,  Fig.  49.  Instruments  designed 
according  to  the  latter  methods  have  the  various  parts  fixed 
relative  to  one  another  and  are  called  'Fixed  Focus  Pyrometers. 

From  an  inspection  of  Fig.  48  it  will  be  seen  that  so  long  as 
the  source  is  not  too  small  to  subtend  the  solid  angle  formed  by  the 


FIG.  47. 


FOSTER  AND  THE  BROWN  FIXED  FOCUS  PYROMETERS      81 

cone  having  0  as  apex,  and  tangent  to  the  orifice  in  the  diaphragm 
A  A',  the  rate  with  which  radiance  is  incident  on  the  receiving 
device  T  is  independent  of  the  distance  from  the  source  to  the 
instrument,  Art.  32.  This  rate  is  the  same  that  would  exist  if  a 
portion  of  the  source  the  size  of  A  A'  were  placed  in  the  orifice  of 


FIG.  48.  FIG.  49. 

the  diaphragm.  For  this  reason  a  fixed  focus  instrument  can  be 
produced  by  having  the  end  diaphragm,  and  the  receiving  device, 
at  the  conjugate  foci  of  a  mirror  or  lens. 

Instead  of  a  concave  spherical  mirror,  a  conical  mirror  may  be 
employed  as  shown  in  Fig.  49.  In  this  case  no  image  of  the  object 
is  formed,  but  the  energy  incident  on  the  receiving  device  T  is  the 
same  as  it  would  be  if  the  orifice  in  the  end  diaphragm  were  filled 
by  a  portion  of  the  source. 

The  millivoltmeter  used  in  connection  with  a  fixed  focus  thermo- 
electric radiation  pyrometer  can  be  provided  with  a  recording 
device  by  means  of  which  a  permanent  record  can  be  made  of  the 
history  of  a  temperature  change. 

35.  The.  Foster  and  the  Brown  Fixed  Focus  Pyrometers.  — 
These  instruments  differ  from  the  Fery  Thermoelectric  Mirror 
Pyrometer  in  that  the  tube  is  longer,  and  the  image  formed  on 
the  thermo junction  is  of  the  orifice  at  the  end  of  the  instrument 
and  not  of  the  hot  object  whose  temperature  is  sought.  That  is, 
the  disc,  T,  attached  to  the  thermoj  unction,  and  the  aperture 
A  A',  Fig.  48,  are  at  the  conjugate  foci  of  the  mirror  M. 

The  object,  mirror,  and  thermocouple  being  in  fixed  posi- 
tions, the  focalizing  rack  and  pinion  of  the  Fe*ry  instrument  is 
dispensed  with.  By  this  device  the  angle  0,  Fig.  44,  is  constant  so 
long  as  the  angle  «,  Fig.  48,  is  subtended  by  the  source.  Thus,  so 
long  as  the  solid  angle  subtended  by  the  source  at  the  point  0,  is 


82  RADIATION  PYROMETRY 

constant,  the  rate  with  which  radiance  is  incident  on  the  thermo- 
j  unction  is  independent  of  the  distance  between  the  source  and 
the  instrument.  A  millivoltmeter  connected  to  the  thermocouple 
indicates  the  temperature  of  the  source.  In  using  the  commercial 
forms  of  this  instrument,  the  distance  of  the  point  0,  from  the 
source  must  not  exceed  ten  times  the  diameter  of  the  source. 


FIG.  50. 

The  range  of  temperatures  that  can  be  measured  by  the  in- 
strument is  modified  by  the  diameter  of  the  aperture  A  A'.  For 
bodies  at  very  high  temperatures  this  aperture  is  small;  for 
bodies  at  lower  temperatures  this  aperture  is  large.  The  same 
millivoltmeter  can  be  used  in  connection  with  apertures  of  different 
sizes,  either  by  having  a  separate  scale  for  each  aperture,  or  by 
having  a  single  scale  and  using  a  different  multiplying  factor  for 
each  aperture. 

The  Brown  pyrometer  differs  from  the  Foster,  Fig.  50,  in  that 
the  tube  is  made  collapsible  for  convenience  of  carrying,  and  a 
finder  is  attached  to  the  tube  for  convenience  in  directing  the 
instrument  toward  the  source  whose  temperature  is  sought. 

36.  Thwing's  Fixed  Focus  Radiation  Pyrometer.  —  In  place 
of  the  gold-plated  spherical  mirror  employed  by  Fery  and  Foster, 
Thwing  has  adopted  a  concave  conical  metal  reflector  M,  Fig.  49, 
in  the  apex  of  which  is  placed  the  thermoelectric  junction  T  con- 
nected to  a  millivoltmeter. 

When  pointed  at  a  hot  body,  practically  all  of  the  radiance  enter- 
ing the  aperture  A  A'  will,  after  multiple  reflection  from  the  sides 
of  the  conical  mirror,  reach  the  thermoelectric  junction.  So  long 


BLACK-BODY  TEMPERATURES  83 

as  the  solid  angle  co  is  subtended  by  the  body  whose  temperature 
is  sought,  the  rate  with  which  radiance  is  incident  on  the  thermo- 
electric junction  is  constant.  The  instrument,  therefore,  requires 
no  focusing.  In  using  the  standard  form  of  this  instrument,  the 
distance  of  the  point  0  from  the  source  must  not  exceed  twelve 
times  the  diameter  of  the  source.  There  is  no  limit  to  the  nearness 
with  which  the  Thwing  Pyrometer  may  be  placed  to  the  hot  body 
except  the  danger  of  injury  due  to  excessive  temperature. 


FIG.  51. 

The  range  of  temperature  that  can  be  measured  by  the  instru- 
ment is  modified  by  the  diameter  of  the  aperture  A  A'.  For 
bodies  at  very  high  temperature,  this  aperture  is  small;  for  bodies 
at  lower  temperatures  this  aperture  is  large.  The  same  milli- 
voltmeter  can  be  used  in  connection  with  apertures  of  different 
sizes,  either  by  having  a  separate  scale  for  each  aperture,  or  by 
having  a  single  scale  and  using  a  different  multiplying  factor  for 
each  aperture. 

As  the  metal  mirror  tarnishes,  the  Thwing  instrument  must  be 
frequently  recalibrated. 

37.  Radiation  Pyrometers  Indicate  Black-body  Tempera- 
tures. —  It  should  be  kept  in  mind  that  radiation  pyrometers 
indicate  black-body  temperatures.  Only  when  a  body  is  radiat- 
ing under  black-body  conditions  is  its  black-body  temperature 
equal  to  the  thermodynamic  temperature.  For  bodies  of  the 
same  radiating  power,  the  black-body  temperatures  will  be  equal 
when  the  thermodynamic  temperatures  are  equal.  But  for  bodies 
of  different  radiating  power,  the  black-body  temperatures  will  not 
be  the  same  when  the  thermodynamic  temperatures  are  equal. 
Only  for  a  body  of  constant  radiating  power  will  the  ratio  of  two 


84  RADIATION  PYROMETRY 

black-body  temperatures  be  equal  to  the  ratio  of  the  thermody- 
namic  temperatures.  A  stream  of  melted  iron  has  a  black-body 
temperature  less  than  that  of  the  same  iron  when  sufficiently 
cooled  to  be  covered  by  a  costing  of  slag  or  oxide. 

A  uniformly  heated  opaque  enclosure  and  a  body  within  such 
an  enclosure  radiates  as  a  black-body.  The  actual  or  thermo- 
dynamic  temperature  of  a  furnace  can  be  obtained  by  directing 
a  radiation  pyrometer  into  a  tube  closed  at  one  end  that  projects 
into  the  region  whose  temperature  is  desired. 

38.  Precautions  in  Using  Radiation  Pyrometers.  —  The  re- 
ceiving instrument  is  subject  to  certain  faults  that  should  be 
^rioted.  After  directing  a  radiation  pyrometer  toward  a  hot 
source;  a  certain  time  is  required  for  the  full  indication  to  be 
developed.  With  different  instruments  of  the  same  model  this 
lag  may  vary  from  20  seconds  to  10  minutes.  In  instruments 
of  a  different  model  the  lag  may  be  less  than  5  seconds.  In  the 
case  of  some  pyrometers  the  deflection  rises  to  a  maximum  and 
then  gradually  diminishes  to  a  fixed  value.  In  using  an  instru- 
ment one  should  take  the  maximum  reading.  For  the  determi- 
nation of  temperatures  that  are  not  constant  an  instrument 
must  be  used  that  has  a  very  small  time  lag. 

The  lag  is  due  to  the  heat  capacity  and  thermal  conductivity 
of  the  receiver.  The  drop  after  the  maximum  deflection  is  due 
to  conduction  of  heat  away  from  the  receiver,  and  in  the  case  of 
a  thermoelectric  receiver,  to  reradiation  and  to  conduction  to  the 
cold  junction. 

The  lag  of  the  Fe*ry  radiation  pyrometers  is  too  great  to  per- 
mit their  use  for  the  determination  of  rapidly  varying  tempera- 
tures. In  the  Thwing  instrument  the  lag  is  lower  than  in  any 
other. 

After  the  instrument  has  been  calibrated,  the  mirror  surface 
must  be  maintained  constant.  Dirt  can  be  removed  with  a 
camel's-hair  brush.  If  the  mirror  becomes  tarnished  the  instru- 
ment must  be  recalibrated. 

In  the  use  of  a  Fe"ry  Thermoelectric  Mirror  Radiation  Pyrom- 
eter serious  error  will  result  if  the  area  of  the  part  of  the  focalizing 


CALIBRATION  OF  A  RADIATION  PYROMETRY  85 

mirrors  covered  by  the  image  is  not  the  same  as  when  the  in- 
strument was  calibrated.  This  is  due  to  the  difference  in  the 
heat  absorbed  by  the  focalizing  mirrors.  If  when  the  instrument 
is  directed  toward  a  body  of  certain  temperature,  a  larger  area 
of  the  focalizing  mirrors  be  covered  by  the  image,  than  when 
the  instrument  was  calibrated,  the  hot  junction  will  be  higher 
in  temperature,  and  the  electromotive  force  developed  by  the 
thermocouple  will  be  greater  than  they  would  be  if  the  instru- 
ment were  used  under  the  conditions  existing  at  the  time  of  the 
calibration.  The  indicated  temperature  will  then  be  too  high. 
The  relation  between  the  fractional  error  in  the  temperature  and 
the  fractional  error  in  the  electromotive  force  is  readily  obtained 
from  (29).  Differentiating,  we  have 

dE  =  abT*-1  dT.  (31) 


Dividing  each  member  of  this  equation  by  the  corresponding 
member  of  (29),  we  obtain 

¥-•?• 

Since  the  value  of  6  is  always  about  4,  this  equation  shows  that 
the  fractional  error  in  the  absolute  temperature  is  about  one- 
fourth  of  the  fractional  error  in  electromotive  force. 

Lack  of  attention  to  this  point  may  readily  produce  an  error 
of  10  to  20  per  cent  in  the  temperature  determination.  The  error 
may  be  obviated  by  placing  the  instrument  at  such  a  distance 
from  the  source  that  the  sharp  image  of  the  source  entirely  covers 
the  focalizing  mirrors. 

Exp.  6.  Calibration  of  a  Radiation  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  29,  30,  37  and  the 
article  describing  the  particular  type  of  pyrometer  under  test. 
Any  radiation  or  optical  pyrometer  can  be  calibrated  by  a  step- 
by-step  comparison  of  the  pyrometer  readings  with  the  readings 
of  a  standardized  thermoelement  in  a  "black-body"  whose  tem- 
perature can  be  varied  through  the  range  for  which  the  pyrometer 


86  RADIATION  PYROMETRY 

is  to  be  used.  In  the  case  of  a  thermoelectric  radiation  pyrom- 
eter exposed  to  the  radiance  from  a  black-body,  the  relation 
between  the  thermodynamic  temperature  of  the  body  and  the 
electromotive  force  developed  is  given  by  (29), 

E  =  aTb,  (29') 

where  a  and  b  are  constants  for  the  particular  instrument.  The 
determination  of  these  constants  require  a  black-body  at  two 
known  temperatures. 

The  object  of  this  experiment  is  to  calibrate  by  the  step-by-step 
method,  and  also  by  means  of  (29)  and  two  known  temperatures, 
a  thermoelectric  radiation  pyrometer  provided  with  an  indicator 
reading  in  millivolts  and  in  degrees  of  temperature.  The  definite 
equation  of  the  temperature-electromotive  force  curve  is  to  be 
determined,  the  curve  represented  by  this  equation  constructed, 
the  empirical  calibration  curve  constructed,  and  also  the  curve 
coordinating  indicated  temperatures  and  corresponding  corrections. 

MANIPULATION.  —  The  apparatus  used  for  the  calibration  in- 
cludes a  complete  radiator,  that  is,  a  "black-body,"  together  with 
a  standardized  thermoelement,  in  connection  with  a  suitable 
millivoltmeter. 

In  using  an  electric  tube  furnace  as  a  "black-body,"  Figs.  37 
and  38,  one  junction  of  a  rhodioplatinum  thermocouple  is  mounted 
in  a  septum  S  of  porcelain  or  graphite  situated  at  the  center  of 
the  tube,  while  the  other  junction  JJf  of  the  couple  is  immersed 
in  a  bath  of  melting  ice. 

After  surrounding  the  "cold  junction"  JJf  with  melting  ice, 
Fig.  52,  close  the  main  switch  W,  and  regulate  the  current  till 
the  millivoltmeter  Vm  indicates  a  temperature  somewhat  lower 
than  the  lowest  one  desired  for  the  calibration.  On  opening  the 
switch,  the  temperature  will  continue  to  rise.  Place  the  pyrometer 
being  calibrated  in  front  of  the  aperture  0,  and  with  the  axis  of  the 
pyrometer  coinciding  with  the  axis  of  the  furnace.  The  distance 
between  the  "black-body"  and  a  Fe*ry  Thermoelectric  Mirror 
Radiation  Pyrometer  must  be  such  that  the  focalizing  mirrors  are 
entirely  covered  by  the  image.  In  the  case  of  the  Fe"ry  Spiral 


CALIBRATION  OF  A  RADIATION  PYROMETRY 


87 


Pyrometer,  the  spiral  must  be  covered  by  the  image.  In  the 
case  of  the  fixed  focus  pyrometers,  the  solid  angle  at  the  pyrom- 
eter subtended  by  the  septum  in  the  furnace  must  not  be  less 
than  the  angular  aperture  of  the  instrument.  In  this  last  case 
the  maximum  allowable  distance  may  be  obtained  by  moving 
the  pyrometer  toward  the  orifice  of  the  "black-body"  till  the 
pyrometer  reading  does  not  increase  with  a  further  diminution 
of  distance. 


FIG.  52. 

When  the  " black-body"'  has  attained  the  lowest  temperature 
to  be  included  on  the  required  calibration  curve,  take  simul- 
taneously the  temperature  reading  of  the  thermoelectric  pyrom- 
eter, the  electromotive  force  reading  and  the  indicated  tempera- 
ture reading  of  the  radiation  pyrometer.  Since  the  temperature 
of  the  septum  lags  behind  the  temperature  of  the  tube,  one  must 
take  no  reading  till  the  thermoelectric  couple  indicates  a  constant 
temperature. 

Again  close  the  switch,  increase  the  current  in  the  electric  fur- 
nace till  the  temperature  is  about  one  hundred  degrees  above  the 
former  temperature,  open  the  switch,  wait  till  the  temperature 
is  practically  constant,  and  then  take  simultaneously  readings  on 
the  two  pyrometers  as  before. 


88  RADIATION  PYROMETRY 

Proceeding  in  this  manner,  take  readings  at  temperature  in- 
tervals of  about  100°  throughout  the  range  for  which  the  instru- 
ment is  to  be  calibrated. 

Construct  a  table  of  six  columns,  in  the  first  column  of  which 
are  given  the  electromotive  forces  as  read  from  the  radiation 
pyrometer  indicator,  in  the  second  column  the  indicated  tem- 
perature read  from  the  same  instrument,  in  the  third  column  the 
electromotive  forces  read  from  the  indicator  connected  to  the 
standard  thermocouple,  in  the  fourth  column  the  thermody- 
namic  temperatures  corresponding  to  these  electromotive  forces, 
in  the  fifth  column  the  difference  between  the  thermodynamic 
temperatures  and  the  temperatures  indicated  by  the  instrument 
under  test,  and  in  the  sixth  column  the  temperature  values  com- 
puted by  means  of  (29)  in  the  manner  now  to  be  described. 

With  the  data  in  column  one  as  ordinates  and  the  data  in 
column  four  as  abscissas  construct  the  empirical  calibration  curve 
of  the  pyrometer  under  test.  By  substituting  in  (29)  the  co- 
ordinates of  two  points  on  this  curve,  the  constants  a  and  b  could 
be  determined. 

These  constants  can  be  determined  more  accurately,  however, 
from  the  equation  Tn  the  form, 

log  #  =  log  a  +  6  log  !T.  (33). 

Using  the  coordinates  of  a  series  of  points  on  the  empirical  cali- 
bration curve,  plot  a  curve  coordinating  log  E  and  log  T.  If  the 
observed  data  are  correct,  this  curve  will  be  a  straight  line.  The 
intercept  on  the  axis  of  ordinates  equals  log  a,  and  the  ratio  of 
the  ordinate  to  the  abscissa  of  any  point  equals  b. 

By  substituting  in  (29)  the  values  of  a  and  b  we  obtain  the 
definite  equation  of  the  calibration  curve.  Using  this  equation 
compute  the  values  of  E  for  a  series  of  convenient  values  of  T. 
Using  these  values  plot  the  computed  calibration  curve  of  the 
instrument  on  the  same  sheet  with  the  previously  drawn  empirical 
calibration  curve. 

With  the  data  in  column  five  as  ordinates  and  the  data  in 
column  four  as  abscissas  plot  the  correction  curve  of  the  given 
pyrometer. 


CHAPTER  V 
OPTICAL  PYROMETRY 

39.  KirchhofiPs  Law.  —  The  ratio  of  the  energy  absorbed  to  the 
energy  incident  on  a  body  is  called  the  absorptive  power  of  the 
body.  An  important  relation  between  the  absorptive  power  of  a 
body  and  the  rate  with  which  it  emits  radiance  was  stated  by 
Kirchhoff.  As  applied  to  monochromatic  radiance  it  may  be 
stated  as  follows :  The  ratio  of  the  rate  of  emission  to  the  absorptive 
power  is  for  all  bodies  the  same  function  of  wave-length  and  thermo- 
dynamic  temperature. 

Thus  representing  the  rate  of  radiation  by  /x,  and  the  absorp- 
tive power  by  the  symbol  a, 

^  =  F  (XT7), 
a 

For  an  opaque  body,  the  sum  of  the  radiance  absorbed  and  the 
radiance  reflected  equals  the  radiance  incident  on  the  body. 
Calling  the  incident  energy  unity,  we  have  for  an  opaque  body 

a  +  r  =  1. 

If  the  body  be  black,  the  reflected  energy  equals  zero.  That 
is>,  for  a  black-body, 

ab  =  1. 

Hence,  ^  [  =  F  (\T) }  =  ^  =  7X6.  (34) 

a  a& 

The  emissive  power  of  a  body  is  the  ratio  of  the  rate  of  radia- 
tion of  energy  by  it,  to  the  rate  of  radiation  of  a  black-body  at 
the  same  thermodynamic  temperature.  Thus,  representing  the 
emissive  power  of  any  given  body  by  the  symbol  e,  we  have, 


90  OPTICAL  PYROMETRY 

Comparing  (34)  with  (35)  we  obtain 

e  =  a.  (36) 

That  is,  the  emissive  power  of  any  body  equals  the  absorptive 
power. 

40.  Wien's  Distribution  Law.  —  When  the  temperature  of  a 
luminous  body  is  increased,  not  only  is  the  total  radiance  in- 
creased but  the  brightness  of  every  part  of  the  spectrum  is  in- 
creased. The  rate  of  radiation  of  energy  7X,  corresponding  to 
visible  radiance  of  wave-length  X,  of  a  black-body  at  absolute 
thermodynamic  temperature  T,  is  expressed  by  Wien's  Distri- 
bution Law, 

/x  =  CiX^e"^,  (37) 


where  e  is  the  base  of  the  natural  system  of  logarithms  and  c\ 
and  c2  are  constants  the  values  of  which  can  be  found  by  meas- 
uring 7X  at  two  known  thermodynamic  temperatures  for  light  of 
known  wave-lengths. 

Wien's  Law  is  a  special  case  of  the  general  radiation  law  derived 
by  Planck  from  purely  thermodynamic  considerations. 


-  l) 


/x  =  CiX-6Vexr  -  I)    .  (38) 

Planck's  Law  apparently  applies  with  exactness  for  any  wave- 
length and  temperature.  Wien's  Law  applies  only  to  wave- 
lengths included  within  the  visible  spectrum,  and  to  temperatures 
within  the  range  that  can  be  produced  artificially.  At  5000° 
absolute,  the  difference  between  the  results  obtained  from  Planck's 
Law  and  Wien's  Law  is  about  one  per  cent. 

Wien's  Distribution  Law  may  be  expressed  in  the  form: 

logio  I\  =  logio  Ci  —  5  logio  X  — 


Or,  representing  the  constant  quantity  (logio  Ci  —  5  logio  X)  by 
the  symbol  Ci,  the  constant  quantity  °2  °gl°  e  by  the  symbol  (72 


THE  THERMODYNAMIC  TEMPERATURE  91 

and  the  Brigg's  or  ordinary  logarithm  by  "log"  without  sub- 
script, this  equation  may  be  put  into  the  abbreviated  form: 

log/x  =  Ci-C2~  (39) 

Experiment   shows   that   when   X   is   expressed   in    microns,* 
c2  =  14,500  (nearly). f 
That  is, 

c  f  _  c2 log  e\ _  14,500  (0.4343)  _  6297  (4Q) 

X     J  X  X 

41.  The  Thermodynamic  Temperature  corresponding  to  a 
given  Black-body  Temperature.  —  The  number  which  represents 
the  temperature  of  a  black-body  on  the  absolute  black-body  scale 
is  that  which  represents  the  same  temperature  on  the  absolute 
thermodynamic  scale.  For- a  nonblack-body  the  number  which 
represents  the  temperature  on  the  black-body  scale  is  less  than 
the  number  which  represents  the  same  temperature  on  the  ther- 
modynamic scale.  The  difference  depends  upon  the  lack  of 
complete  absorptive  power  of  the  surface  of  the  body. 

A  black-body  temperature  measured  from  the  absolute  zero  in 
centigrade  degrees  by  means  of  radiance  of  all  frequencies  emitted 
by  the  hot  body  is  often  represented  by  the  symbol  K,  e.g., 
1200°  K.  And  if  measured  by  means  of  radiance  of  a  single 
frequency  it  is  represented  by  the  symbol  K\,  where  X  is  the  wave- 
length in  air  of  the  radiance.  For  example,  1200°  K.&  represents 
a  black-body  temperature  measured  by  means  of  radiance  of 
wave-length  in  air  of  0,65  microns. 

Consider  a  nonblack-body  at  a  temperature  according  to  the 
absolute  black-body  scale  of  K\°,  and  according  to  the  thermo- 
dynamic scale  of  T°.  The  relation  between  T  and  K\  will  now 
be  deduced. 

*  The  micron  is  one-thousandth  of  a  millimeter  and  is  represented  by  the 
symbol  n. 

t  Other  determinations  of  this  constant  give  the  values  c  =  14,250  and 
14,360. 


92  OPTICAL  PYROMETRY 

Suppose  the  given  nonblack-body  be  first  within  a  uniformly 
heated  opaque  enclosure,  and  later  be  without  the  enclosure  but 
the  same  thermodynamic  temperature.  When  within  the  en- 
closure and  in  thermal  equilibrium  with  it,  the  body  is  at  some 
thermodynamic  temperature  T  and  is  radiating  energy  of  wave- 
length X  at  the  rate  IXb,  given  by  Wien's  Distribution  Law  (39), 

log/x6  =  C1-C2|.  (41) 

When  at  the  same  thermodynamic  temperature,  but  outside  of 
the  heated  enclosure,  the  same  body  is  at  some  black-body  tem- 
perature K\,  and  is  radiating  at  a  less  rate  7\,  given  by  Wien's 
Distribution  Law. 

log/x  =  Ci-  C2j£  •  (42) 

Subtracting  from  each  member  of  (42)  the  corresponding 
member  of  (41)  we  obtain 

r    ~\  r -i  in 

(43) 

By  definition,  the  ratio  of  the  rate  of  radiation  of  any  body  to 
the  rate  of  radiation  of  a  black-body  at  the  same  thermodynamic 
temperature  is  the  emissive  power  of  the  given  body.  It  has 
been  shown  (36)  that  the  emissive  power  of  any  body  equals 
the  absorptive  power.  Consequently  the  above  equation  can  be 
put  into  the  form : 

log  a  =  C2  --  — 


T'K 

On  substituting  for  C2  its  value  (40),  we  have 

where  T  denotes  the  absolute  thermodynamic  temperature  that 
corresponds  to  the  black-body  temperature  K\  of  a  body  that 


THE  THERMODYNAMIC  TEMPERATURE 


93 


absorbs  radiance  of  wave-length  X  at  the  rate  a.    It  should  be 
noted  that  in  this  equation  X  is  expressed  in  microns. 


0.50 


0.40 


0.50 


0.60 
Emissiwty 

FIG.  53. 


0.70 


o.so 


0.90 


It  is  found  that  absorptive  power  varies  considerably  with  the 
wave-length,  but  only  slightly  with  temperature.  Consequently, 
knowing  the  absorptive  power  of  a  given  substance  for  radiance 


94  OPTICAL  PYROMETRY 

of  a  particular  wave-length,  together  with  the  black-body  tem- 
perature deduced  from  a  determination  of  the  rate  of  emission 
by  the  body  of  radiance  of  the  same  wave-length,  we  can  compute 
the  thermodynamic  temperature  of  the  body. 

The  wave-length  of  light  usually  employed  in  optical  pyrom- 
eters is  X  =  0.65  M-  Using  (44),  the  corrections  to  be  added  to 
readings  of  optical  pyrometers  using  light  of  wave-length  X  = 
0.65  v,  for  a  series  of  values  of  emissivity,  have  been  computed  * 
and  the  results  here  plotted  in  the  curves  of  Fig.  53.  Knowing 
the  value  of  emissivity  of  the  substance,  the  true  or  thermo- 
dynamic temperature,  corresponding  to  any  apparent  or  black- 
body  temperature  can  be  found  from  these  curves  without  further 
computation.  For  example,  liquid  or  incandescent  solid  iron 
and  steel  free  from  oxide  has  an  emissivity  of  from  0.37  to  0.40. 
So,  that,  assuming  the  latter  value,  a  stream  of  iron  at  an  ap- 
parent temperature  of  1400°  C.  would  have  a  true  or  thermo- 
dynamic temperature  of  1523°  C.  Again  since  solid  iron  oxide 
has  an  emissivity  of  0.92  the  curves  show  that  the  true  tempera- 
ture of  an  ingot  is  practically  the  same  as  the  apparent  tempera- 
ture obtained  by  an  optical  or  radiation  pyrometer. 

Liquid  iron  oxide  has  an  emissivity  of  0.53;  liquid  slag,  from 
0.55  to  0.75,  depending  upon  the  composition,  —  "dark"  slag 
being  about  0.65.  The  emissivity  of  nickel  is  about  that  of  iron. 
That  of  liquid  copper  0.15  and  of  solid  copper  0.11. 

42.  The  Equality  of  Brightness  Method  of  Measuring  Tem- 
peratures. —  The  brightness  of  a  luminous  source  is  measured 
by  the  rate  of  emission  of  luminous  radiance  per  unit  area,  and 
depends  upon  the  temperature.  When  not  above  3000°  C., 
Wien's  Distribution  Law  (39)  expresses  with  considerable  accu- 
racy the  relation  between  the  black-body  temperature  of  a  source 
and  the  rate  with  which  it  emits  luminous  radiance  for  any  speci- 
fied wave-length.  Hence,  from  a  comparison  of  the  brightness 
for  any  particular  wave-length  of  two  bodies,  one  can  determine 
the  ratio  of  the  black-body  temperatures  of  the  given  bodies. 
The  method  of  determining  temperatures  from  a  comparison  of 
*  Burgess  —  Technologic  Papers  of  the  Bureau  of  Standards,  No.  91. 


THE  EQUALITY  OF  BRIGHTNESS 


95 


the  brightness  or  the  color  of  bodies  is  called  Optical  Pyrometry. 
An  instrument  that  compares,  for  a  particular  color,  the  bright- 
ness of  a  hot  body  with  the  brightness  of  a  standard  lamp,  and 
which  is  calibrated  so  as  to  indicate  temperatures,  is  called  an 
Equality  of  Brightness  Optical  Pyrometer. 

If  an  image  is  formed  of  a  luminous  source,  the  quantity  of 
energy  of  any  particular  wave-length  in  unit  area  of  the  image  is 
a  constant  fraction  of  the  energy  of  the  same  wave-length  emitted 
during  the  same  time  from  unit  area  of  the  source,  if  the 
distance  from  the  source  to  the  objective  of  the  pyrometer  be 
constant.  When  either  a  lens  or  a  mirror  is  employed,  the 
brightness  of  the  image  is  independent  of  the  distance  of  the 
lens  or  mirror  from  the  source  so  long  as  the  lens  or  mirror  sub- 
tends the  same  solid  angle  at  a  point  of  the  image.  Whence, 
the  ratio  of  the  luminous  energy  per  unit  area  of  two  sources 
can  be  obtained  from  a  comparison  of  the  brightness  of  the  images 
of  the  sources. 


FIG.  54. . 

) 

It  will  now  be  shown  that  the  constancy  of  the  angular  aper- 
ture of  a  lens  or  mirror  can  be  maintained  by  the  use  of  a  dia- 
phragm having  an  opening  of  fixed  area,  at  a  fixed  distance  from 
the  image.  In  Fig.  54,  the  image  of  the  point  S  is  formed  at 
F,  and  is  observed  by  means  of  the  eyepiece  E.  In  an  ordinary 
telescope  the  distance  of  the  image  from  the  eyepiece  changes 


96  OPTICAL  PYROMETRY 

when  the  distance  of  the  object  changes,  and  the  eyepiece  must 
be  moved  forward  or  back  correspondingly.  Instead  of  this 
procedure,  the  eyepiece  might  be  fixed,  and  the  image  main- 
tained in  the  proper  position  relative  to  the  eyepiece  by  moving 
the  objective.  If,  in  addition,  there  be  a  diaphragm  D,  with 
an  opening  of  constant  area  A,  at  a  fixed  distance  I,  from  the 
image,  then  whatever  may  be  the  distance  from  the  object  to 

the  telescope,  the  solid  angle  subtended  at  the  image  by  the 

^ 
objective  will  be  — ,  which  is  a  constant  quantity  henceforth  to 

L 

be  represented  by  the  symbol  w. 

It  is  essential  that  an  optical  pyrometer  should  have: 

(a)   an  invariable  standard  light  source; 

(6)   an  appliance  for  producing  nearly  monochromatic  light; 

(c)  a  sensitive  photometric  screen; 

(d)  a  method  for  varying  continuously  and  by  a  known  amount 
the  brightness  of  either  one  source  or  its  image. 

The  luminous  source  used  as  a  standard  of  comparison  must  be 
invariable  in  color  and  brightness.  Incandescent  electric  lamps, 
and  the  flames  of  amyl  acetate,  gasoline,  kerosene,  and  acetylene 
are  employed  as  standard  light  sources. 

Monochromatic  light  is  best  produced  by  means  of  a  prism. 
Usually,  however,  colored  glasses  are  used  that  give  light  which 
is  nearly  monochromatic.  Since  the  absorptive  power  of  colored 
glass  is  different  for  light  of  different  wave-lengths,  if  there  is 
any  lack  of  monochromatism  in  the  colored  glasses,  Wien's 
Distribution  Law  will  not  apply.  If  the  colored  glass  transmits 
two  bands  or  one  wide  band,  the  value  of  the  absorption  factor 
will  be  different  at  different  temperatures. 

Optical  pyrometers,  like  total  radiation  pyrometers,  compare 
black-body  temperatures.  In  case  two  luminous  sources  radiate 
under  black-body  conditions,  the  ratio  of  their  black-body  tem- 
peratures equals  the  ratio  of  their  thermodynamic  temperatures. 
If  the  temperature  of  a  " black-body"  has  been  adjusted  till  the 
standard  lamp  of  an  optical  pyrometer  and  the  "black-body" 
have  the  same  brightness  for  light  of  a  particular  wave-length, 


THE  GENERAL  OPTICAL  PYROMETER  EQUATION         97 

and  then  the  optical  pyrometer  is  sighted  on  another  body  radi- 
ating under  black-body  conditions,  the  ratio  of  the  thermody- 
namic  temperatures  of  the  "black-body"  and  the  body  under 
investigation  can  be  obtained.  If,  in  addition,  the  thermody- 
namic  temperature  of  the  " black-body"  is  known,  then  the 
thermodynamic  temperature  of  the  other  black-body  can  be 
computed.  Wherever  possible  bodies  are  observed  when  radi- 
ating under  black-body  conditions.  The  thermodynamic  tem- 
perature of  a  steel  ingot  can  be  obtained  directly  from  an  obser- 
vation of  its  brightness  while  it  is  in  the  soaking  pit.  On  removal 
from  the  uniformly  heated  enclosure,  the  ingot  will  no  longer 
radiate  as  a  black-body  and  an  observation  of  its  brightness  will 
give  not  thermodynamic  temperature,  but  black-body  tempera- 
ture. If,  however,  its  black-body  temperature  together  with 
the  absorptive  power  of  its  surface  be  known,  the  thermody- 
namic temperature  can  be  computed  from  (44). 

43.  The  General  Optical  Pyrometer  Equation.  —  Represent- 
ing by  7X  the  rate  with  which  radiance  of  wave-length  X  leaves 
unit  area  of  a  hot  source,  and  by  J\  the  rate  with  which  this 
radiance  is  incident  on  unit  area  of  the  image, 

/A  =  */A,  (45) 

where  z  is  a  constant  of  proportionality. 

Frequently  the  brightness  of  the  image  of  either  the  source  or 
the  comparison  lamp  is  too  intense.  In  this  event,  one  or  more 
absorptive  glasses  can  be  used  to  diminish  the  intensity  of  the 
transmitted  light.  Let  J\  be  the  rate  with  which  energy  of 
wave-length  X  is  incident  on  unit  area  of  the  image  when  an 
absorptive  glass  is  used.  Then  we  write: 

Jx  =  fliJx',  (46) 

where  Ri  is  called  the  Absorptive  Factor  of  the  glass  plate. 

If  a  second  piece  of  absorptive  glass  having  an  absorptive 
factor  #2  be  added  to  the  first  plate,  then 

J\  =  RZ  (Ri  J\), 
and  if  several  absorptive  glasses  are  added: 

Jx  =  (RiR*R*  '  '  •)  Jx'.  (47) 


98  OPTICAL  PYROMETRY. 

Substituting  this  value  in  (45), 

Ix  =  2  (RiRtR*  •  •  •  )  A'.  (48) 


On  substituting  this  value  in  Wien's  Distribution  Law  (39),  we 
have 


log  Ix  =  ft-         =  log  z+  (log  /2i 
whence  the  black-body  temperature 


=  _    _ 
ft  -  log  z  -  (log/2!  H-  log  £2  +  log  /28  +  •   •  •)  -  log  J/ 

or,  representing  the  constant  quantity  (ft  —  log  z)  by  the  symbol 
C3  we  obtain  the  general  equation  of  optical  pryometry, 


C* 


C3  -  (log  Ri  +  log  #2  +  log  £3  +  •  •  •)  -  log  Jx' 


In  case  the  image  of  the  hot  source  is  less  bright  than  that  of 
the  comparison  lamp,  absorptive  glasses  can  be  placed  in  the 
path  of  light  from  the  comparison  lamp.  In  this  case,  the  term 
within  the  parenthesis  is  positive. 

The  value  of  C2  is  given  in  (40).  By  methods  to  be  hereafter 
described,  the  values  of  the  other  quantities  in  the  right-hand 
member  can  be  experimentally  determined  by  means  of  the 
various  optical  pyrometers. 

It  should  be  noted  that  the  K\  in  (49)  represents  temperature 
according  to  the  black-body  scale.  If  the  emitting  surface 
radiates  as  a  black-body  then  the  number  which  represents  the 
temperatures  according  to  the  black-body  scale  equals  that 
which  represents  the  temperature  according  to  the  thermody- 
namic  scale,  that  is,  the  symbol  K^  can  be  replaced  by  T.  Also, 
if  the  emitting  surface  radiates  as  a  black-body,  the  temperature 
obtained  from  (49)  will  be  the  same  whatever  be  the  wave-length 
of  the  light  used  in  the  measurement. 

An  inspection  of  the  Table  of  Absorptive  Powers,  also  shows 
that  the  absorptive  powers  of  nonblack-bodies  is  different  for 
radiance  of  different  wave-lengths.  From  this  it  follows  that 


THE  GENERAL  OPTICAL  PYROMETER  EQUATION        99 

the  monochromatic  black-body  temperature  determined  by  means 
of  radiance  of  one  wave-length  is  not  the  same  as  that  at  a  dif- 
ferent wave-length.  From  (49)  the  same  conclusion  is  evident;  — 
that  is,  if  the  emitting  surface  does  not  radiate  as  a  black-body, 
different  values  of  K\  will  be  obtained  according  to  the  wave- 
length of  light  used  in  the  measurement.  For  this  reason,  in 
the  case  of  nonblack-bodies,  it  is  necessary  to  know  the  wave- 
length of  the  light  employed  in  the  measurement.  Light  of  any 
conveniently  obtained  wave-length  may  be  employed.  But  since 
when  the  temperature  of  a  body  is  raised  till  the  body  becomes 
incandescent,  red  is  the  first  color  that  appears,  it  follows  that 
by  using  red  light  lower  temperatures  can  be  compared  than  by 
using  light  of  any  other  color.  There  is  a  brand  of  glass  that 
absorbs  almost  completely  light  of  all  wave-lengths  except 
X  =  0.65  IJL.  This  glass  is  now  commonly  used  in  optical  pyrom- 
etry  as  a  light  filter.  For  this  reason  it  is  customary  to  use 
light  of  this  wave-length  in  optical  pyrometry  even  though  a 
prism  is  used  instead  of  colored  glass  to  produce  the  monochro- 
matic light. 

Since  the  energy  in  the  infra  red  part  of  the  spectrum  greatly 
exceeds  that  in  the  visible  part,  and  since  the  absorptive  power 
(and  emissive  power)  of  nonblack-bodies  is  less  for  the  infra  red 
than  for  the  visible  radiance,  it  follows  that  the  rate  of  emission 
of  visible  radiance  from  nonblack-bodies  is  more  nearly  equal  to 
the  rate  of  emission  of  visible  radiance  from  a  black-body  than 
is  the  rate  of  emission  of  the  total  radiance  of  nonblack-bodies 
equal  to  the  rate  of  emission  of  total  radiance  from  a  black-body. 
Consequently  an  optical  pyrometer  calibrated  against  a  black- 
body  will  give  readings  of  the  temperature  of  a  nonblack-body 
that  are  nearer  thermodynamic  temperatures  than  will  a  radia- 
tion pyrometer. 

The  optical  pyrometers  now  in  use  are  essentially  photometers 
for  comparing  the  brightness  of  a  spot  of  light  from  the  hot  source 
whose  temperature  is  sought  with  that  of  a  spot  of  light  from  a 
comparison  lamp.  The  differences  between  the  various  types  of 
optical  pyrometers  consist  in  the  different  types  of  comparison 


100  OPTICAL  PYROMETRY 

lamp  and  in  the  methods  of  bringing  to  a  photometric  balance 
the  light  from  the^two  sources.^ 

44.  The  Color  Identity  Method  of  Measuring  Temperature.  — 
The  radiating  power  of  a  body  is  directly  proportional  to  its 
absorbing  power.     A  body  of  perfect  absorbing  power  for  radiance 
of  all  frequencies  is  said  to  be  black.     A  body  that  has  an  ab- 
sorbing power  less  than  unity,  but  which  is  the  same  for  all  fre- 
quencies is  said  to  be  gray.  •  The  color  of  a  body  depends  only 
upon  the  relative  amounts  of  light  of  the  various  frequencies 
radiated:!  the  brightness  depends  upon  the  absolute  amounts. 
The  brightness  of  gray  bodies  is  less  than  that  of  black-bodies 
at  the  same  thermodynamic  temperature,  but  the  color  of  the 
light  emitted  by  all  black  and  all  gray  bodies  at  the  same  ther- 
modynamic temperatures  is  the  same.     The  fact  that  black  and 
gray  bodies  at  the  same  thermodynamic  temperature  are  of  the 
same  color  is  the  basis  of  a  system  of  pyrometry  called  the  Color 
Identity  Method  of  Measuring  Temperatures. 

The  determination  of  the  temperature  of  a  given  body  by 
this  method  consists  in  varying  the  temperature  of  a  calibrated 
black  or  gray  body  till  it  has  the  same  color  as  the  given  body. 
The  temperature  of  the  standard  body  is  then  that  of  the  body 
under  test.  The  standard  of  comparison  is  a  "black-body" 
whose  thermodynamic  temperature  is  under  control  and  that  can 
be  obtained  by  means  of  a  calibrated  thermoelectric  pyrometer. 
A  secondary  standard  of  greater  convenience  in  ordinary  meas- 
urements is  a  carbon  filament  incandescent  lamp  for  which  the 
thermodynamic  temperatures  at  various  currents  have  been  pre- 
viously determined  by  matching  the  color  against  that  of  a 
"  black-body." 

45.  Le  Chatelier's  Optical  Pyrometer.  —  The  first  successful 
instrument  for  determining  the  temperature  of  a  luminous  source 
from  a  photometric  comparison  with  a  standard  lamp  consists  of 
a  telescope  furnished  with  a  side  branch  in  which  the  standard 
lamp  is  placed.    When  in  use,  light  from  the  body  whose  tem- 
perature is  to  be  determined,  and  light  from  the  standard  lamp, 
form  images  side  by  side,  in  the  focal  plane  of  the  eyepiece. 


LE  CHATELIER'S  OPTICAL  PYROMETER         .  .    101 

These  images  are  brought  to  equality  of  brightness  by  means  of 
an  iris  diaphragm  in  front  of  the  objective.  Approximate  mono- 
chromatic light  is  produced  by  colored  glasses.  By  means  of 
the  general  optical  pyrometer  equation,  the  indications  of  this 
instrument  can  be  transformed  into  black-body  temperatures. 

When  directed  toward  a  luminous  object,  light  traverses  the 
iris  diaphragm,  D,  Fig.  55,  and  the  objective  0.  The  part  of 
the  beam  that  grazes  the  edges  of  the  mirror  M  forms  an  image 
of  the  source  in  the  focal  plane  of  the  eyepiece  E.  Light  from 


FIG.  55. 


FIG.  56. 


the  comparison  lamp  L  forms  an  image  of  the  standard  flame 
in  the  focal  plane  of  the  eyepiece,  and  by  means  of  the  mirror 
M  is  reflected  into  the  eyepiece  E.  These  two  images,  side  by 
side,  and  separated  only  by  a  sharp  line,  are  observed  by  means 
of  the  eyepiece  E  provided  with  a  red  filter  R  for  rendering  of 
approximately  the  same  wave-length  the  light  that  enters  the 
eye  from  the  two  images.  The  brightness  of  the  image  of  the 
source  is  brought  to  equality  with  that  of  the  image  of  the  com- 
parison flame  by  means  of  the  iris  diaphragm  D.  In  case  the 
source  under  investigation  is  very  intense,  the  brightness  of  the 
image  of  the  source  is  reduced  by  means  of  absorptive  glasses 
G.  In  case  the  source  under  investigation  is  less  bright  than 


102 


OPTICAL  PYROMETRY 


the  standard  flame,  an  absorptive  glass  is  placed  in  the  path 
of  the  light  from  the  standard  flame  instead  of  in  the  path  of  the 
light  from  the  source.  By  the  use  of  one  or  more  absorptive 
glasses,  the  same  instrument  may  be  used  for  a  wide  range  of 
temperature  measurements. 

46.  The  Fery  Absorption  Pyrometer.  —  This  instrument, 
Figs.  57  and  58,  includes  a  pair  of  wedges  of  absorptive  glass 
ww',  an  objective  0,  a  diaphragm  of  fixed  aperture  D,  a  Lummer- 
Brodhun  prism  xy,  a  comparison  lamp  L,  objective  0',  totally 
reflecting  prism  P,  ocular  E  and  red  filter  glass  R. 


FIG.  57. 


FIG.  58. 


The  Lummer-Brodhun  prism  consists  of  two  right-angled 
prisms.  The  hypothenuse  face  of  y  is  completely  polished, 
while  that  of  x  has  an  unpolished  round  central  spot.  Light 
from  the  left  incident  upon  the  central  portion  of  the  hypothe- 
nuse faces  will  not  be  transmitted,  whereas  light  incident  out- 
side of  this  spot  will  be  transmitted  to  the  ocular.  Light  from 
the  comparison  lamp  incident  upon  the  central  spot  of  the  hy- 
pothenuse faces  will  be  totally  reflected  into  the  ocular,  whereas 
that  incident  outside  of  this  spot  will  be  transmitted  to  one  side 
of  the  instrument. 


THE  SHORE  PYROSCOPE 


103 


On  looking  through  the  ocular  focalized  on  the  center  of  the 
hypotheneuse  faces,  one  sees  a  central  round  patch  of  light  from 
the  comparison  lamp,  surrounded  by  a  ring  of  light  from  the 
source  under  investigation.  If  the  brightness  of  the  source  is 
not  much  greater  than  that  of  the  standard,  the  two  images  can 
be  brought  to  equality  of  brightness  by  sliding  the  absorbing 
wedges.  A  scale  attached  to  the  wedges  indicates  the  thickness 
of  absorptive  glass  traversed  by  light  from  the  source.  After 
the  instrument  has  been  calibrated,  the  divisions  on  this  scale 
will  indicate  black-body  temperatures.  The  range  of  the  Fe>y 
Optical  Pyrometer  may  be  extended  by  the  use  of  absorptive 
glasses  G  and  G',  as  in  the  case  of  the  Le  Chatelier  instrument. 

The  diaphragm  D  ensures  a  fixed  angular  aperture  so  that  no 
correction  need  be  made  for  lack  of  focus,  or  for  varying  distance 
from  the  source. 


FIG.  59. 

47.  The  Shore  Pyroscope.  —  Various  modifications  of  the 
Le  Chatelier  pyrometer  have  been  devised  by  Shore,  Fe"ry,  and 
others.  In  the  Shore  Pyroscope,  Figs.  59  and  60,  the  brightness 
of  the  image  of  the  source  under  investigation  is  maintained  less 
than  that  of  the  comparison  flame  by  means  of  a  diaphragm  A  of 
fixed  aperture  placed  in  front  of  the  objective.  Light  from  the 
source,  after  traversing  the  diaphragm  of  fixed  aperture  A,  the  red 


104 


OPTICAL  PYROMETRY 


filter  G,  and  the  objective  0,  forms  an  image  in  the  focal  plane  of 
the  eyepiece.  Light  from  the  comparison  flame  L,  after  travers- 
ing the  objective  0',  a  red  filter  G',  iris  diaphragm  D,  and  ground 
glass  diffusing  screen  S,  is  reflected  by  the  tiny  mirror  M  and  forms 

an  image  in  the  focal  plane  of  the 
eyepiece.  The  objectives  are  pro- 
tected by  the  cover  glasses  C  and  C'. 
On  looking  through  the  eyepiece, 
one  sees  the  image  of  an  element  of 
the  comparison  flame  in  the  center 
of  the  image  of  the  source  whose 
temperature  is  sought.  The  bright- 
ness of  the  image  of  the  comparison 
flame  is  reduced  to  that  of  the  source 
by  means  of  the  iris  diaphragm  oper- 
ated by  the  milled  head  H.  The 
jaws  of  the  iris  diaphragm  D  have 
such  a  form  that  equal  spaces  on  the 
divided  circle  attached  to  them  repre- 
sent equal  differences  on  the  black- 
body  temperature  scale. 

The  Shore  Pyroscope  is  focalized  by  moving  the  objective  by 
means  of  the  knurled  head  F.  Though  there  is  no  diaphragm 
between  the  objective  and  the  image,  this  arrangement  makes  the 
angular  aperture  of  the  objective  so  nearly  constant  that  there  is 
no  serious  error  introduced  by  changing  the  distance  between  the 
instrument  and  the  body  whose  temperature  is  sought. 

48.  The  Morse  Thermogauge  or  Holborn-Kurlbaum  Op- 
tical Pyrometer.  —  This  instrument  differs  from  those  of  the 
Le  Chatelier  type  in  that  instead  of  projecting  the  image  of  the 
comparison  source  on  the  focal  plane  of  the  objective,  the  compari- 
son source  itself  is  placed  there,  and  its  brightness  is  adjusted  to 
equality  with  the  brightness  of  the  image  of  the  source  whose 
temperature  is  sought. 

The  comparison  source  L,  Fig.  61,  is  a  4-volt  electric  incandes- 
cent lamp  placed  in  the  focal  plane  of  the  objective  0.  The 


FIG.  60. 


THE  WANNER  OPTICAL  PYROMETER  105 

current  is  adjusted  by  means  of  a  rheostat  in  circuit  with  the 
lamp.  In  using  the  instrument,  the  telescope  is  directed  to  the 
source  whose  temperature  is  sought;  the  objective  0  is  moved 
back  and  forth  till  the  image  of  the  source  is  in  the  plane  of  the 
filament  of  the  electric  lamp, 
and  the  current  is  adjusted  till 
the  tip  of  the  filament  just  dis- 
appears against  the  bright  back- 
ground.  When  this  occurs,  the 

temperature  of  the  filament  equals  the  apparent  black-body 
temperature  of  the  image.  Thus,  the  value  of  the  current  when 
the  tip  of  the  filament  is  invisible  is  a  measure  of  the  black-body 
temperature  of  the  source. 

The  light  that  reaches  the  eye  is  rendered  approximately  mono- 
chromatic by  a  red  glass  R.  When  bodies  at  very  high  tempera- 
ture are  observed,  the  light  is  so  dazzling  that  the  brightness  is 
reduced  by  one  or  more  absorptive  glasses  placed  in  front  of  the 
objective.  Excessive  heating  of  the  filament  of  the  comparison 
lamp  is  thereby  also  obviated. 

The  diaphragm  D  at  a  fixed  distance  from  the  image  of  the 
source  renders  the  angular  aperture  of  the  objective  constant. 
Thus  the  brightness  of  the  image  of  the  source  is  independent 
of  the  distance  of  the  telescope  from  the  source. 

The  original  Morse  Thermogauge  was  without  diaphragm  or 
lenses.  The  present  form  of  the  instrument  is  provided  with 
these  important  improvements  due  to  Holborn  and  Kurlbaum. 

49.  The  Wanner  Optical  Pyrometer.  —  In  the  Wanner 
Pyrometer,  light  from  the  source  whose  temperature  is  sought, 
and  light  from  a  comparison  source,  are  drawn  out  into  two 
spectra.  From  these  two  spectra,  two  narrow  stripes  of  the  same 
width  and  the  same  wave-length  are  isolated  and  the  intensities 
of  these  stripes  are  compared  by  means  of  a  polarizing  device. 
Light  from  the  hot  source  traverses  the  cover  glass  C  and  the 
slit  Si,  Fig.  62,  while  light  from  the  comparison  lamp  L,  after 
traversing  a  diffusing  glass,  is  reflected  by  the  mirror  M  into  the 
slit  $2-  Each  beam -is  rendered  parallel  by  the  objective  0,  and 


106 


OPTICAL  PYROMETRY 


each  is  spread  out  into  a  spectrum  by  the  direct  vision  prism  F. 
The  Rochon  double  image  prism  R  separates  each  beam  into 
two  beams,  polarized  in  planes  at  right  angles  to  one  another. 
Each  of  these  beams  falling  on  both  faces  of  the  wide  angled 


•J 


FIG.  62. 

prism  B  is  again  divided  into  two.  The  Wanner  Optical  Pyrom- 
eter is  essentially  a  double-slit  direct-vision  spectroscope  to  which 
has  been  added  the  polarizing  prism  R,  analyzing  prism  A,  and 
wide  angled  prism  B  cemented  to  the  ocular  Oi. 

If  the  polarizer  R  and  wide  angled  prism  B  were  not  present 
there  would  be  formed  in  the  plane  of  the  diaphragm  S,  a  spec- 
.  „  trum  due  to  light  that  had  traversed 
,.  '2*  the  slits  Si  and  S*.  In  Fig.  63,  these 
h*  I2"  spectra  are  represented  by  "1"  and 
!"l  \i*  "2"  respectively.  With  the  Rochon 
4  |i«  polarizing  prism  R  in  place,  each  of 
4  these  spectra  is  divided  into  two,  — 
\  one  consisting  of  plane  polarized  light 
with  the  vibrations  vertical,  and  the  other  with  the  vibrations 
horizontal.  In  the  diagram,  these  spectra  are  represented  by 
the  symbols  1V)  1A,  2«,  2h.  With  the  wide  angled  prism  B  in 
place,  all  four  beams  impinge  on  both  faces  of  the  prism.  The 
parts  of  the  four  beams  that  strike  the  upper  face  of  the 
double  image  prism  will  be  refracted  downward.  On  emer- 
gence these  parts  are  distinguished  in  the  diagram  by  "primes." 
The  parts  of  the  beam  that  strike  the  lower  face  will  be  bent 


FIG.  63. 


WIDE  FILAMENT  PYROMETER  COMPARISON  LAMP      107 

upward.  *  On  emergence  these  parts  are  distinguished  in  -  the 
diagram  by  "  seconds." 

The  four  beams  that  strike  the  upper  half  of  the  wide  angled 
prism  emerge  side  by  side  and  are  focalized  by  the  lens  0\  in  the 
plane  of  the  diaphragm  S.  In  the  same  manner,  the  four  beams 
that  strike  the  lower  half  of  the  wide  angled  prism,  emerge  side 
by  side  and  are  focalized  by  the  lens  0\  in  the  plane  of  the  dia- 
phragm S.  The  wide  angled  prism  B  is  so  tilted  that  these  two 
rows  of  spectra  will  not  be  superposed  but  will  form  two  bands 
side  by  side  and  in  the  same  plane.  In  Fig  63,  the  two  rows  of 
spectra  (2h'}  2V',  lh',  I/)  and  (2A",  2/',  1,",  I/O  should  not  be  in 
different  planes  as  there  represented,  but  should  be  in  one  plane 
perpendicular  to  the  page.  In  the  eyepiece  diaphragm  S,  there 
is  a  slit  parallel  to  the  slits  Si  and  82,  which  cuts  off  all  the  light 
except  a  narrow  stripe  out  of  the  red  from  one  of  the  ordinary 
beams  that  originated  at  the  hot  source,  and  a  similar  stripe  of 
the  same  wave-length  from  one  of  the  extraordinary  beams  that 
originated  at  the  comparison  source. 

The  field  of  view  of  the  instrument  is  thus  divided  into  two 
halves  by  a  sharp  division  line.  One  half  of  the  field  is  illumined 
by  plane  polarized  light  from  the  hot  source,  while  the  other 
half  is  illumined  by  light  coming  from  the  comparison  lamp 
polarized  in  the  plane  at  right  angles  to  the  first.  By  inter- 
posing a  Nicol  prism  A,  Fig.  62,  between  the  diaphragm  and  the 
eye,  the  two  halves  may  be  brought  to  equal  brightness. 

The  comparison  lamp  L  is  a  6-volt  incandescent  lamp  "aged" 
by  being  operated  for  several  hours  at  an  excessive  voltage.  By 
means  of  a  rheostat  and  ammeter,  the  current  in  the  comparison 
lamp  can  be  adjusted  to  give  constant  brightness. 

It  should  be  added  that  in  some  Wanner  Optical  Pyrometers, 
a  piece  of  red  glass  is  used  to  produce  approximately  monochro- 
matic light  instead  of  the  dispersing  prism  described  above. 

50.  The  Wide  Filament  Pyrometer  Comparison  Lamp. — 
Optical  as  well  as  radiation  pyrometers  can  be  calibrated  by 
means  of  a  " black-body"  operated  at  a  series  of  known  tempera- 
tures. Electrically  heated  tube  furnaces,  however,  are  expensive 


108  OPTICAL  PYROMETRY 

to  maintain  and  they  lack  portability  and  ease  of  operation. 
These  objections  do  not  apply  to  a  wide  filament  incandescent 
lamp  capable  of  being  operated  at  high  temperatures.  By  means 
of  a  calibrated  optical  pyrometer  and  ammeter,  the  black-body 
temperature  of  the  wide  filament  when  traversed  by  various 
known  currents  can  be  obtained.  Such  a  calibrated  pyrometer 
comparison  lamp  can  be  used  instead  of  a  " black-body"  for  the 
calibration  of  optical  pyrometers  as  seen  in  Fig.  69. 

Exp.  7.   Calibration  of  a  Le  Chatelier  Optical  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  40,  42,  43,  45. 
When  an  electrically  heated  tube  furnace  provided  with  a  cali- 
brated thermocouple  is  at  hand,  any  pyrometer  can  be  calibrated 
directly  throughout  the  range  of  the  furnace.  Often,  however, 
such  a  step-by-step  method  is  inconvenient  or  impossible.  In 
the  following  paragraphs  it  will  be  shown  how  a  calibration  curve 
of  the  Le  Chatelier  Optical  Pyrometer  can  be  constructed  from 
a  single  temperature  observation.  The  object  of  this  experi- 
ment is  to  construct  the  calibration  curve  of  a  Le  Chatelier  Opti- 
cal Pyrometer  by  the  step-by-step  method,  and  also  by  means 
of  a  single  temperature  observation  and  an  equation  now  to  be 
derived. 

When  the  objective  lens  0,  Fig.  55,  is  directed  toward  the 
body  whose  temperature  is  sought,  and  the  comparison  lamp  L 
is  maintained  at  constant  brightness,  a  photometric  balance  can 
be  obtained  by  varying  the  brightness  of  the  image  of  the  hot 
source  by  means  of  the  iris  diaphragm  D.  The  length  d,  of  one 

side  of  the  square  aperture  of  the  dia- 
phragm is  observed  on  the  scales  at- 
tached to  the  two  jaws. 

Let  0,  Fig.  64,  represent  a  luminous 
object  of  effective  area  A0',  i,  its  image 
of  area  At-;   and  D  a  diaphragm  con- 
taining a  square  aperture  having  a  side  of  length  d.    If  the  rate 
of  radiation  per  unit  area  of  the  source  be  represented  by  /x,  and 


LE  CHATELIER  OPTICAL  PYROMETER  109 

the  rate  with  which  radiance  of  wave-length  X  is  incident  on 
the  image  when  there  is  no  absorptive  glass  be  represented  by  J\, 


Also,  Jx<x  d2, 

where  d  is  the  length  of  one  side  of  the  aperture. 

Then  Jx  =  C'^-°d2. 


u 


T  1/2 

That  is,  h  =  C'  (50) 

But  from  a  property  of  lenses, 


A0        U2 

---      or 


A{      v2  v* 

On  substituting  this  value  in  (50) 

,3T. 

(51) 


If  absorptive  glasses  having  absorptive  factors,  Ri,  R^  and  R^ 
etc.,  be  interposed  between  the  objective  and  the  image,  then  the 
rate  with  which  energy  of  wave-length  X  is  incident  on  unit  area 
of  the  image  has  a  value  Jx'  given  by  the  relation  (47) 

Jx  =  (R\  RZ  Rz  •   •   •)  J\* 
And  the  preceding  equation  becomes 

h=^r£  (Biftfc...).  (52) 

A.  {ft 

If  in  the  experiment,  the  brightness  of  the  image  be  kept  con- 

j  t 

stant  by  regulating  the  diaphragm,  then  the  quantity  -£-  is  con- 

Ai 

stant.  If,  in  addition,  the  instrument  be  kept  at  a  fixed  distance 
from  the  source,  v2  is  constant.  Then,  under  these  experimental 
conditions,  the  above  equation  becomes 

•     •    •) 


110 


OPTICAL  PYROMETRY 


Substituting  this  value  in  Wien's  Distribution  Law  (39),  we 
have, 

log  7X 1"=  Ci  -  |?j  =  log  C"  +  log  R!  +  log  #2  +  log  R3  -  2  logd, 

whence, 

n. 

(53) 


where  C4  represents  the  constant  quantity  (Ci  —  log  C"). 

Before  (53)  can  be  used  to  measure  temperatures,  the  con- 
stants Cz  and  £4  must  be  determined.  And  if  absorptive  glasses 
are  used,  their  absorptive  factors,  Ri,  R2,  Rs,  etc.,  must  also  be 
known. 

MANIPULATION.  —  Fill  the  comparison  lamp  with  gasoline, 
light  the  wick  and  adjust  the  position  of  the  flame  till  the  field 
of  view  in  the  eyepiece  due  to  the  comparison  flame  is  uniformly 
bright.  Focalize  the  telescope  of  the  instrument  on  the  red  hot 
carbon  block  in  the  electrically  heated  "  black-body  "  which 
supports  the  hot  junction  of  a  calibrated  thermocouple.  Note 


FIG.  65. 

the  reading  on  the  scale  engraved  on  the  telescope  tube  when 
the  instrument  is  in  focus.  The  calibration  now  to  be  obtained 
will  apply  only  when  the  telescope  is  of  this  particular  length. 

By  means  of  an  ice  bath,  not  shown  in  Fig.  65,  keep  the  cold 
junction  of  the  thermoelectric  pyrometer  at  a  constant  tem- 
perature. 


LE  CHATELIER  OPTICAL  PRYOMETER  111 

At  a  known  temperature,  as  low  as  it  is  possible  to  make  set- 
tings, take  a  reading  of  the  aperture  without  the  absorptive  glass 
and  also  with  the  absorptive  glass.  Increase  the  temperature  by 
25°  intervals  for  four  settings  and  take  a  similar  pair  of  readings 
at  each  temperature.  Now  increase  the  temperature  by  50°  inter- 
vals as  far  as  desired,  and  take  similar  pairs  of  readings.  From 
these  observations  construct  on  one  pair  of  coordinate  axes,  the 
step-by-step  calibration  curve  of  the  instrument  without  absorp- 
tive glass,  and  also  the  one  with  the  absorptive  glass.  Lay  off 
temperatures  along  the  axis  of  abscissas,  and  diaphragm  aper- 
tures along  the  axis  of  ordinates. 

The  calibration  curve  is  now  to  be  constructed  by  means  of 
the  law  of  the  instrument  expressed  in  (53).  The  constants  C2 
and  C4  can  be  obtained  if  we  know  the  wave-length  of  the  light 
transmitted  by  the  monochromatic  filter  glass  R,  Fig.  55,  to- 
gether with  the  length  of  one  side  of  the  iris  diaphragm  D  when 
the  standard  flame  balances  photometrically  the  light  from  a 
body  of  known  temperature.  If  the  wave-length  of  the  light 
transmitted  by  the  filter  glass  is  not  known,  the  constants  C%  and 
(74  can  be  determined  from  readings  obtained  from  a  body  at 
two  known  temperatures.  The  former  method  is  susceptible  of 
greater  precision  and  will  be  first  considered. 

To  obtain  €2,  the  wave-length  of  the  light  transmitted  by  the 
filter  glass  is  most  easily  obtained  by  means  of  a  direct  vision 
spectroscope  with  scale  of  wave-lengths.  Then,  (40), 

6297 


Knowing  C2,  together  with  the  value  of  d,  corresponding  to  one 
known  temperature,  the  value  of  C4  can  be  determined.  For 
this  purpose,  note  the  coordinates  d  and  K\  of  any  convenient 
point  of  the  previously  obtained  calibration  curve.  If  no  ab- 
sorptive glass  be  used,  Ri  =  R%  =  R$  =  0.  In  this  case,  the 
values  of  C2,  Kx  and  d,  now  at  hand,  substituted  in  (53)  will  give 
us  the  value  of  C4.  The  value  of  C4  thus  obtained  will  hold  so 
long  as  the  conditions  involved  in  (53)  are  fulfilled. 


112  OPTICAL  PYROMETRY 

If  an  absorptive  glass  be  used,  the  absorptive  factor,  RI  can 
be  found  as  follows:  Direct  the  instrument  toward  a  frosted 
globe  incandescent  lamp  or  other  uniformly  bright  constant  light 
source;  bring  the  two  halves  of  the  field  of  view  to  equal  bright- 
ness and  note  the  length  di  of  one  side  of  the  aperture  in  the 
diaphragm.  Then  insert  the  absorptive  glass;  obtain  a  photo- 
metric balance,  and  note  the  new  length  d%  of  the  aperture. 

When  no  absorptive  glass  was  used,  we  have,  (51),j 

7x-2g;  (54) 

and  when  one  absorptive  glass  was  used  having  an  absorptive 
factor  Rij  we  have,  (52), 


During  these  two  measurements  the  intensity  of  the  source 
/x  is  constant.  And  since  the  brightness  of  the  image,  in  both 
cases,  is  that  of  the  comparison  flame,  J\  =  J\.  Whence, 
equating  the  right-hand  members  of  (54)  and  (55),  we  obtain 


If  several  absorptive  glasses  are  used,  the  absorptive  factor  of 
each  may  be  separately  determined  as  above. 

Now  that  all  the  constants  of  (53)  have  been  determined, 
values  of  K\  corresponding  to  a  series  of  values  of  d  can  be  com- 
puted. From  such  a  table  of  values  of  K\  and  d}  construct  a 
curve  coordinating  black-body  temperatures  and  pyrometer 
readings. 

On  the  sheet  with  the  step-by-step  calibration  curve,  lay  off 
temperatures  along  axis  of  abscissas,  and  diaphragm  apertures 
along  axis  of  ordinates.  This  curve  should  coincide  with  the  one 
previously  obtained. 

Sometimes  no  instrument  is  at  hand  for  the  determination  of 
the  wave-length  of  the  light  used.  If  two  known  temperatures  are 
available,  the  constants  C2  and  C4  can  be  determined  with  a  fair 


LE  CHATELIER  OPTICAL  PYROMETER  113 

• 

degree  of  accuracy  even  though  X  is  unknown.     Thus,  suppose 
that  at  temperatures  K\  and  K\",  when  no  absorptive  device  is 
used,  the  scale  readings  are  di  and  dz,  respectively. 
Then  from  (53) 


Whence,  solving  for  C*  by  eliminating  €2, 


On  substituting  the  numerical  values  of  C2  and  C4,  together 
with  the  values  of  the  absorptive  factors  of  any  glasses  that  may 
be  used,  a  series  of  definite  values  of  d  can  be  computed  that 
correspond  to  any  assigned  values  of  K^.  From  a  series  of  cor- 
responding values  of  d  and  K\  thus  obtained,  a  calibration  curve 
can  be  drawn. 

In  either  of  the  manners  above  described  a  calibration  curve 
is  to  be  constructed,  when  the  instrument  is  provided  with  an 
absorptive  glass,  and  another  when  it  is  not. 

It  should  be  noted  that  the  Le  Chatelier  Optical  Pyrometer  is 
focalized  by  moving  the  objective  instead  of  by  moving  the  eye- 
piece. But  as  there  is  no  diaphragm  between  the  objective  and 
the  image,  the  angular  aperture  of  the  objective  is  not  quite 
constant  when  the  distance  from  the  instrument  to  the  object  is 
changed.  The  error  thereby  introduced  into  temperature  deter- 
minations is,  however,  always  small.  For  example,  if  the  dis- 
tance from  the  telescope  to  the  object  be  changed  by  25  per  cent, 
then  even  without  refocalizing,  the  error  would  be  only  about  5 
per  cent. 

The  commercial  form  of  Le  Chatelier's  instrument  cannot  be 
focalized  on  an  object  nearer  than  about  three  feet.  When  the 
instrument  is  used  at  a  minimum  distance,  the  object  must  be 
not  less  than  6  mm.  on  a  side. 


114  OPTICAL  PYROMETRY 

Exp.  8.   Calibration  of  a  Wanner  Optical  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  40,  42,  43,  and  49. 
A  calibration  curve  can  be  constructed  from  a  series  of  obser- 
vations of  scale  readings  corresponding  to  a  large  number  of 
known  temperatures.  Oftentimes,  however,  it  is  impossible  to 
produce  such  a  series  of  known  temperatures  throughout  the 
range  for  which  it  is  desired  to  use  the  instrument.  In  the  fol- 
lowing paragraphs  it  will  be  proved  that  a  calibration  curve  can 
be  constructed  from  the  discussion  of  data  obtained  from  the 
observation  of  a  black-body  at  but  one  known  temperature. 
The  object  of  this  experiment  is  to  construct  a  curve  coordinating 
black-body  temperatures  of  a  luminous  object  with  the  scale 
readings  of  a  Wanner  Optical  Pyrometer,  first,  by  the  step-by- 
step  method,  and  second  by  means  of  Wien's  Distribution  Law 
and  a  reading  made  on  a  black-body  at  known  temperature. 

It  will  first  be  shown  that  when  the  two  halves  of  the  field  of 
view  are  of  equal  brightness,  the  angle  between  the  plane  of 
polarization  of  the  analyzer  A,  Fig.  62,  and  the  plane  of  polari- 
zation of  the  light  in  the  half  of  the  field  of  view  due  to  the  source, 
is  a  measure  of  the  ratio  of  the  brightness  of  the  two  sources. 

It  will  then  be  shown  that  by  intro- 
ducing this  result  into  the  general 
optical  pyrometer  equation,  the  ratio 
of  the  black-body  temperatures  of  any 
bodies  can  be  determined. 
^  In  Fig.  66,  let  OM  be  the  plane  of 
polarization  of  light  in  the  half  of  the 
J  field  of  view  coming  from  the  hot 
source  and  let  ON  be  the  plane  of  polarization  of  the  light  in 
the  other  half  coming  from  the  comparison  source.  Let  OH 
and  OC  represent  the  amplitudes  of  vibration  of  the  light  con- 
stituting these  two  halves  of  the  field  of  view.  Let  OQ  be  the 
plane  of  transmission  of  the  Nicol  prism  when  the  two  halves  of 
the  field  of  view  are  of  equal  brightness.  This  equality  requires 
that  the  angle  6  must  be  such  that  the  projection  of  OC  on  OQ 


c 
FIG.  66. 


CALIBRATION   OF  A  WANNER  OPTICAL  PYROMETER      115 

equals  the  projection  of  OH  on  OQ.  That  is,  OQ  is  perpendicular 
to  HC.  It  follows  that 

OG  =  OH  cos  0  =  OCsin0. 

That  is,  the  amplitudes  of  vibration  of  the  light  in  the  field  of 
view  of  the  instrument  coming  from  the  two  sources  are  in  the 

ratio  Qfj 

—  -tan  9. 

Representing  the  brightness  of  the  field  of  view  due  to  the  hot 
source  by  J\  and  the  brightness  of  the  field  of  view  due  to  the 
comparison  source  by  J\",  and  remembering  that  brightness 
varies  directly  with  the  square  of  the  amplitude  of  vibration, 
we  have 

(60) 


Since  at  45°  the  value  of  the  tangent  of  an  angle  changes  least 
with  a  given  change  of  angle,  the  indications  of  a  Wanner  pyrom- 
eter are  most  sensitive  when  the  angle  between  the  polarizer  and 
analyzer  is  45°.  Or  expressed  in  another  way  —  at  around  45° 
small  changes  of  intensity  will  necessitate  large  movements  of  the 
index  hand,  while  in  the  neighborhood  of  0°  or  90°  smaller  move- 
ments of  the  index  hand  would  be  required.  When  the  tempera- 
ture of  the  hot  source  is  much  higher  than  that  of  the  comparison 
source,  the  angle  0  will  be  much  greater  than  45°  and  the  readings 
will  be  lacking  in  sensitiveness.  To  obviate  this,  an  absorptive 
glass  may  be  placed  in  the  path  of  the  light  from  the  hot  source. 

Since  the  Wanner  Optical  Pyrometer  compares  the  luminous 
intensity  of  radiance  of  the  same  wave-length  from  two  sources, 
the  ratio  of  the  black-body  temperatures  of  the  two  sources  can 
be  obtained  by  means  of  Wien's  Distribution  Law.  Let  mono- 
chromatic light  from  the  hot  source  be  photometrically  balanced 
against  light  of  the  same  wave-length.  Substituting  in  the  gen- 
eral equation  of  optical  pyrometry  (49)  the  value  of  J\  given  in 
(60)  we  obtain  for  the  Wanner  Optical  Pyrometer, 


_  _       _ 

X  "  C3  -  (logft  +  log£2  +  ...)-  log  Jx"  -  log  tan2  0 


116  OPTICAL  PYROMETRY 

When  the  brightness  of  the  comparison  lamp  is  constant,  the 
quantity  (C3  —  log  Jx")  is  constant  and  may  be  represented  by 
the  symbol  €5.  Whence, 

C 


C5  -  (logffi  +  Iogfl2  +   •••)-  Iogtan20 


If  the  absorptive  glasses  are  not  used,  the  quantity  within  the 
parenthesis  becomes  zero.  Assuming  this  arrangement,  the  com- 
parison lamp  at  constant  brightness,  and  the  constants  X,  C^  and 
€5  known,  a  series  of  values  of  0  can  be  substituted  in  this  equa- 
tion, and  the  corresponding  values  of  K\  computed.  These  values 
can  be  conveniently  coordinated  by  a  curve.  If  now  the  py- 
rometer be  directed  toward  an  incandescent  body  of  known 
black-body  temperature  K^,  the  analyzer  set  at  the  angle  6  which 
the  previously  constructed  curve  shows  corresponds  to  this  value 
of  KX,  and  the  current  in  the  comparison  lamp  adjusted  till  the 
two  halves  of  the  field  of  view  are  equally  bright,  the  pyrometer 
will  be  in  adjustment  with  the  previously  constructed  curve. 

If,  thereafter,  the  comparison  lamp  be  maintained  at  its  pres- 
ent brightness,  the  black-body  temperature  of  any  incandescent 
body  can  be  obtained.  The  operation  consists  in  directing  the 
instrument  toward  the  hot  source,  rotating  the  analyzer  till  a 
photometric  balance  is  obtained,  observing  the  angle  6,  and 
looking  up  on  the  calibration  curve  or  table  the  temperature  that 
corresponds  to  the  particular  angle. 

If  the  range  of  the  instrument  is  to  be  increased  by  the  use  of 
absorptive  glasses  placed  between  the  hot  body  and  the  pyrom- 
eter then  in  (61)  the  term  within  the  parenthesis  does  not  become 
zero.  Consequently,  in  calculating  the  temperatures  for  various 
values  of  0  we  shall  have  to  know  the  numerical  values  of  Ri, 
Rz,  etc.  From  (46)  we  see  that  with  a  single  absorptive  glass  of 
absorptive  factor  Ri, 

#i=7V  (62) 

J\ 

where  J\  represents  the  brightness  of  the  field  of  view  due  to  the 
hot  source  when  no  absorptive  glass  is  interposed,  and  J\   rep- 


CALIBRATION  OF  A  WANNER  OPTICAL  PYROMETER      117 

resents  the  brightness  when  an  absorptive  glass  of  absorptive 
factor  RI  is  interposed. 

If  the  brightness  of  the  field  of  view  due  to  the  comparison 
lamp  be  denoted  by  J\",  then  from  (60) 

Jx  =  A"  tan2  0, 
and  Jx'  =  /A"  tan2  6'. 

Whence  (62), 

This  equation  shows  that  to  determine  the  absorptive  factor 
RI  of  a  piece  of  glass  it  is  only  necessary  to  direct  the  Wanner 
Optical  Pyrometer  toward  any  uniformly  luminous  source,  rotate 
the  Nicol  until  a  photometric  balance  is  obtained,  read  the  angle  6; 
then  after  interposing  the  absorptive  glass  between  the  pyrom- 
eter and  the  luminous  source,  balance  the  fields  again  and  read 
0'.  These  values  substituted  in  (63)  give  the  numerical  value  of 
the  absorptive  factor. 

MANIPULATION.  —  To  find  the  temperature  Kx,  by  means  of 
(61)  it  is  necessary  to  experimentally  determine  the  wave-length 
of  light  transmitted  by  the  instrument,  together  with  the  absorp- 
tive factor  of  each  absorptive  glass  used  in  front  of  the  objective. 

As  the  slit  in  the  ocular  of  the  pyrometer  is  fairly  wide,  the 
field  of  view  is  not  strictly  monochromatic,  but  is  a  more  or  less 
narrow  band  in  the  red  portion  of  the  spectrum  formed  by  the 
prism.  The  wave-lengths  of  the  light  at  the  edges  of  the  band 
must  be  found  and  their  mean  taken  as  the  value  of  X.  The 
most  convenient  method  of  measuring  the  wave-lengths  is  by  the 
use  of  the  spectrometer  provided  with  a  scale  of  wave-lengths. 
Have  the  pyrometer  directed  toward  the  sun,  an  arc  lamp  or 
other  intense  light  source,  and  place  in  front  of  the  eyepiece  a 
direct-reading  spectrometer.  On  looking  into  the  eyepiece  of 
the  spectrometer  a  bright  band  will  be  seen.  On  the  scale  of  the 
spectrometer  the  wave-lengths  of  the  edges  can  be  read. 

To  determine  the  absorptive  factor  of  an  absorptive  glass, 
direct  the  pyrometer  toward  a  frosted  globe  incandescent  lamp 
or  other  convenient  nearly  uniformly  lighted  surface,  and  set  the 


118  OPTICAL  PYROMETRY 

current  in  the  comparison  lamp  at  any  convenient  value  which 
must  be  maintained  constant  while  taking  the  following  obser- 
vations. Balance  the  photometric  fields  and  read  the  angle. 
Place  the  plate  of  absorptive  glass  in  front  of  the  objective,  again 
obtain  a  balance  and  read  the  angle.  From  the  values  of  these 
two  angles  calculate  RI  from  (63).  . 

With  the  already  measured  value  of  X  calculate  C2  from  (40). 

Since  the  indications  of  a  Wanner  pyrometer  are  most  sensitive 
when  the  angle  between  the  polarizer  and  analyzer  is  45°,  and 
since  by  properly  adjusting  the  intensity  of  the  comparison  lamp 
the  two  fields  can  be  balanced  at  45°  for  a  wide  range  of  tempera- 
tures of  the  hot  source,  it  will  be  convenient  to  adjust  the  com- 
parison lamp  till  the  reading  is  45°  for  the  particular  temperature 
at  which  most  precise  readings  are  desired.  Assuming  some 
temperature  K*,  at  which  6  is  to  be  45°  without  absorptive  glasses, 
and  knowing  the  value  of  X  and  of  C^  the  value  of  €5  can  be 
computed  from  (61). 

Substitute  the  values  of  €2  and  C&,  now  determined,  in  (61), 
and  compute  the  temperatures  corresponding  to  various  angles 
extending  from  10°  to  80°  at  intervals  of  5°  when  no  absorptive 
glasses  are  used. 

Also  compute  the  temperatures  for  the  same  angles  when  one 
absorptive  glass  of  known  absorptive  factor  is  used. 

The  following  concrete  example  will  illustrate  the  method.  Let  it  be 
required  to  construct  a  calibration  curve  for  a  Wanner  Optical  Pyrometer 
arranged  to  be  most  sensitive  for  a  temperature  of  900°  C.  It  was  found  by 
measurement  that  the  band  transmitted  by  this  particular  instrument  extends 
from  X  =  0.674  /*  to  X  =  0.638  ».  The  means  of  these  values  gives  X  = 
0.656  M. 

From  (40) 


Since  we  wish  to  make  the  most  sensitive  part  of  the  scale  at  900°  C.,  then 
at  45°  the  value  of  K\  is  to  be  900  +  273=  1173.  From  (61)  we  have,  when 
no  absorptive  glasses  are  used: 

9599 


c6  -  0  -  0 
Whence 

C6  =  8.183. 


CALIBRATION  OF  A  WANNER  OPTICAL  PYROMETER      119 


Knowing  the  values  of  C2  and  Cs  we  can  calculate  the  values  of  K\  corre- 
sponding to  various  angles. 

The  data  obtained  for  determining  Ri  were  as  follows: 
6  =  63°, 
0'  =  58°.5. 

Therefore  (63),  ft-dsnfj- 

log  #1  =  log  tan2  63°  -  log  tan2  58°.5 
=  0.58566  -  0.42536 
=  0.16. 

We  are  now  prepared  to  find  the  temperature  that  corresponds  to  any 
regular  setting  6  when  no  absorptive  glass  is  used  and  also  when  one  is  used 
having  the  absorptive  factor  just  determined. 

From  (61),  without  the  absorptive  glass,  a  setting  of  the  analyzer  at  the 
angle  6  =  20°  corresponds  to  a  black-body  temperature 
9599 


8.18  -0.16  -  (-0.88) 


=  1077°  absolute  =  804°  centigrade. 


In  this  manner  make  the  necessary  computations  and  construct 
a  table  for  values  of  6  extending  from  10°  to  80°  with  5°  intervals 
as  indicated  below. 


I 

Log  tan2  0 

Log  Ri  =  0 

Log  Ri  =  0.16 

tfx  abs. 

Kx  cent. 

#x'abs. 

.K^'cent. 

10° 

15° 

20° 

-0.88 

1059° 

786° 

1077° 

804° 

25° 

With  temperatures  as  abscissas  and  angles  as  ordinates,  plot 
two  curves  on  the  same  sheet  coordinating  0  with  K\  centigrade 
and  6  with  K\  centigrade.  These  curves  are  the  calibration 
curves  of  the  instrument  with  and  without  the  particular  absorp- 
tive glass  plate  used  above. 

To  make  the  above  calibration  curves  of  use  in  measuring 
temperatures  it  is  necessary  that  the  current  through  the  com- 
parison lamp  be  set  at  a  definite  value  which  must  be  kept  con- 
stant when  the  pyrometer  is  used  thereafter. 


120  OPTICAL  PYROMETRY 

To  find  the  value  of  this  current,  heat  the  "black-body"  up 
to  a  temperature  well  within  the  range  of  the  instrument.  Sight 
the  pyrometer  on  the  septum  that  supports  the  hot  end  of  the 
thermoelectric  couple  and  note  the  temperature  by  means  of  an 
indicator  connected  to  the  standard  thermocouple  in  the  furnace. 
From  the  calibration  curve  just  obtained  find  the  angle  corre- 
sponding to  the  thermodynamic  temperature  of  the  furnace.  Set 
the  analyzer  of  the  pyrometer  at  this  angle,  and  regulate  the 
current  in  the  comparison  lamp  till  the  two  halves  of  the  field 
of  view  in  the  pyrometer  eyepiece  are  equally  bright.  Note 
the  value  of  the  current  now  in  the  comparison  lamp.  When 
the  pyrometer  is  used  thereafter  to  determine  temperatures,  the 
current  must  be  maintained  at  this  value. 


FIG.  67. 

To  verify  the  calibration  curves  plotted  above,  heat  the 
"black-body"  to  several  different  temperatures  and  take  the 
readings  of  the  standard  thermoelement  simultaneously  with  the 
settings  of  the  analyzer.  Make  each  setting  with  and  without 
the  absorptive  glass.  On  the  sheet  containing  the  calibration 
curves,  plot  the  series  of  points  obtained  from  the  settings  of 
the  analyzer  and  the  temperature  observed  with  the  thermo- 
element, when  no  absorptive  glass  was  used,  and  another  similar 
series  curve  when  an  absorptive  glass  was  used. 

Instead  of  reading  angles  and  then  finding  the  temperatures 
from  a  previously  constructed  calibration  curve,  it  is  common 
practice  to  divide  the  circular  scale  of  the  instrument  so  as  to 
indicate  black-body  temperature  directly.  If  the  instrument 


CALIBRATION  OF  A  WANNER  OPTICAL  PYROMETER     121 


being  calibrated  is  provided  with  both  a  scale  in  degrees  and  a 
scale  in  temperatures  a  Table  of  Corrections  should  be  constructed. 

Since  the  Wanner  Pyrometer  makes  use  of  a  polarizing  device 
for  the  equalization  of  the  brightness  of  two  light  beams,  polarized 
light  should  not  enter  the  instrument.  Most  incandescent  sur- 
faces emit  partially  polarized  light,  but  the  degree  of  polarization 
of  the  light  emitted  normal  to  surface  is  the  minimum.  Hence, 
the  Wanner  Pyrometer  should  be  directed  normally  to  the  hot 
surface  whose  temperature  is  sought. 

Since  the  images  observed  are  of  the  slits  of  the  instrument 
and  not  of  the  source  sighted  upon,  no  focusing  is  required  for 
various  distances  from  the  object.  Care  must  be  exercised  that 
the  pyrometer  is  sufficiently  near  the  object  that  the  field  of  view 
due  to  the  object  shall  be  uniformly  bright.  To  prevent  the 
instrument  being  overheated,  the  model  sold  under  the  trade 
name  "Scimatco"  is  enclosed  in  a  double-walled  metal  case  as 
illustrated  in  Figs.  62  and  67. 

If  after  calibration,  the  comparison  lamp  should  change  in 
brightness,  the  calibration  curve  would  no  longer  apply.  But 
the  constancy  of  the  electric  comparison  lamp  can  be  readily 
checked  at  any  time  by  comparison  with  a  flame  of  constant 
intensity.  For  example,  at  the  time  of  calibration  let  the  optical 
pyrometer  be  directed  toward  the  flame  of  a  standard  amyl 
acetate  pyrometer  lamp,  and  the 
analyzing  Nicol  prism  be  turned 
till  the  two  halves  of  the  field  of 
view  in  the  eyepiece  are  equally 
bright.  The  present  setting  of 
the  analyzer  is  called  the  Normal 
Point  of  the  particular  instru- 
ment. With  the  Nicol  at  the 
normal  point,  if  at  any  subse- 
quent tune  the  instrument  be  directed  toward  the  standard  flame, 
the  two  halves  of  the  field  of  view  should  be  equally  bright. 
If  this  is  not  the  case,  the  current  in  the  comparison  lamp  should 
be  adjusted  till  equality  of  brightness  is  attained.  After  this 


FIG.  68. 


122  OPTICAL  PYROMETRY 

adjustment,  the  previously  obtained  calibration  curve  will  apply 
to  readings  of  the  instrument. 

In  making  the  check,  the  pyrometer  and  the  standard  amyl 
acetate  lamp  are  placed  in  the  carrying  case,  at  definite  positions 
marked  by  the  maker.  The  height  of  the  flame  is  adjusted  till 
the  tip  can  just  be  seen  when  the  line  of  sight  A B  is  as  indicated 
in  Fig.  68. 

Exp.  9.   Calibration  of  a  Holborn-Kurlbaum  Optical  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  40,  42,  43,  and  48. 
The  object  of  this  experiment  is  to  construct  a  calibration  curve 
of  a  Holborn-Kurlbaum  Optical  Pyrometer,  first,  by  the  step- 
by-step  method,  then  by  means  of  the  general  optical  pyrometer 
equation  and  three  known  temperatures. 

The  theory  of  the  latter  method  will  now  be  considered.  It 
depends  upon  the  fact  that  the  relation  between  the  current 
through  a  carbon  filament  and  its  black-body  temperature  varies 
with  each  filament,  but  in  all  cases  is  represented  for  a  consider- 
able range  by  a  formula  of  the  type, 

i  =  a  +  bt  +  ct2,  (64) 

where  i  represents  the  current  (usually  expressed  in  milliamperes), 
t  represents  the  black-body  temperature  in  centigrade  degrees, 
and  a,  b,  c  are  constants  depending  upon  the  filament.  To 
determine  these  three  constants  the  temperature  must  be  known 
for  three  known  values  of  the  current.  By  means  of  this  relation 
a  calibration  curve  can  be  extended  beyond  the  temperature 
range  through  which  measurements  have  been  made.  We  will 
now  obtain  the  equation  connecting  the  temperature  K\,  of  a 
body  that  produces  an  image  of  certain  brightness  when  no 
absorptive  device  is  used,  and  the  temperature  K\  that  the  body 
would  need  to  have  in  order  that  the  image  may  be  of  the  same 
brightness  when  an  absorptive  device  is  used. 

Let  I\  be  the  rate  of  emission  of  energy  of  wave-length  X  by 
the  source  whose  absolute  black-body  temperature  is  K*. 


HOLBORN-KURLBAUM  OPTICAL  PYROMETER          123 

Then  by  (39) 

Ci--  (65) 


If  J\  be  the  rate  at  which  energy  emerges  from  the  objective, 
then  7X  =  z/x'.  (66) 

Now  let  an  absorptive  glass  of  absorptive  factor  R  be  placed  in 
front  of  the  objective  and  let  the  temperature  of  the  source  be 
raised  until  the  rate  at  which  energy  emerges  from  the  objective 
is  the  same  as  before.  Then  if  Kxf  is  the  present  temperature 
of  the  source,  and  I\  is  the  rate  of  emission  of  energy  of  wave- 
length X  from  the  source  at  this  temperature, 

log/x^Ci-IV  (67) 

AX 

and  /x'  =  zRJ*'.  (68) 

Subtracting  from  each  member  of  (67)  the  corresponding  member 
of  (65) 

lo 

Substituting  from  (66)  and  (68)  into  (69) 


-F-*'-  (70) 

U2  AX         A\ 

Setting  -  ;  —  =  Ce,  we  obtain 
62 


(71) 

AX  -A-X 

This  equation  gives  the  relation  between  the  black-body  tem- 
perature A~x  of  a  source  that  produces  an  image  of  a  certain  bright- 
ness, and  the  black-body  temperature  AY  that  the  source  would 
need  to  have  in  order  that  light  from  it  after  traversing  an  ab- 
sorptive medium  shall  form  an  equally  bright  image.  Equation 
(64)  gives  the  relation  between  the  current  in  the  comparison 


124 


OPTICAL  PYROMETRY 


lamp  and  the  black-body  temperature  of  the  filament.  When 
the  comparison  lamp  filament  .is  of  the  same  brightness  as  the 
image  of  the  source,  the  temperature  of  the  comparison  lamp 
equals  the  apparent  temperature  of  the  image.  Whence,  if  the 
filament  has  a  constant  radiating  power,  the  same  equation  with 
different  values  for  the  constants  will  express  the  relation  between 
the  current  in  the  comparison  lamp  and  the  black-body  tempera- 
ture of  the  sources  sighted  upon. 

MANIPULATION.  —  Direct  the  Holborn-Kurlbaum  Optical  Py- 
rometer to  the  wide  filament  of  a  calibrated  pyrometer  lamp, 
Art.  50.  Adjust  the  pyrometer  till  the  top  of  the  filament  in 
the  eyepiece  is  superposed  on  the  image  of  the  wide  filament  of 
the  pyrometer  lamp,  and  till  there  is  no  motion  of  one  relative 
to  the  other  when  the  eye  is  moved  from  one  side  to  the  other  in 
front  of  the  eyepiece. 

With  no  absorptive  glass  between  the  wide  filament  pyrometer 
lamp  and  the  objective  of  the  optical  pyrometer,  first  adjust  the 


FIG.  69. 

current  in  the  wide  filament  pyrometer  lamp  till  the  filament  is 
dull  red.  Then  adjust  the  current  in  the  comparison  lamp  in  the 
eyepiece  of  the  pyrometer  till  the  tip  of  the  filament  disappears 
against  the  back-ground  formed  by  the  image  of  the  wide  fila- 
ment of  the  pyrometer  lamp.  Note  the  current  in  the  wide 
filament  pyrometer  lamp  and  the  current  in  the  comparison 


HOLBORN-KURLBAUM  OPTICAL  PYROMETER          125 

lamp.  Also,  from  the  calibration  curve  of  the  wide  filament 
pyrometer  lamp,  note  the  present  black-body  temperature  of  the 
filament.  In  the  same  manner,  take  simultaneous  readings  of 
the  current  in  the  comparison  lamp  and  in  the  wide  filament 
pyrometer  lamp  at  intervals  of  about  100°  C.  throughout  the 
range  of  the  wide  filament  pyrometer  lamp. 

With  these  data  plot  as  abscissas  values  of  K\  according  to  the 
centigrade  scale,  and  as  ordinates  values  of  i  expressed  in  milli- 
amperes.  This  is  the  empirical  calibration  curve  of  the  instru- 
ment, when  no  absorptive  glass  is  used.  The  equation  of  this 
curve  is  of  the  form  (64).  From  the  coordinates  of  three  points 
of  the  curve  compute  the  constants  a,  6,  and  c.  The  definite 
equation  obtained  by  substituting  these  values  in  (64)  is  the 
equation  of  the  calibration  curve  when  no  absorptive  glass  is 
used.  Only  three  known  temperatures  are  required  to  construct 
this  curve.  Check  this  equation  by  computing  values  of  i  cor- 
responding to  a  series  of  assigned  values  of  Kx,  according  to  the 
centigrade  scale,  at  100°  intervals  from  600°  C.,  to  1500°  C.  On 
the  same  sheet  with  the  empirical  calibration  curve  plot  this 
computed  calibration  curve  and  compare  the  two  curves. 

The  calibration  curve  of  the  instrument  when  an  absorptive 
glass  is  used  is  -now  to  be  computed.  Find  the  wave-length  X 
of  the  light  transmitted  by  the  instrument  by  means  of  a  spec- 
trometer provided  with  a  scale  of  wave-lengths.  Knowing  X, 
the  constant  C2  as  given  by  (40)  is 

6297 


The  absorptive  factor  can  be  determined  by  means  of  a  Wanner 
Pyrometer  as  described  in  exp.  8,  or  by  means  of  any  spectro- 
photometer.  Knowing  C2  and  R,  the  value  of  Ce  is  determined 
by  its  value 


With  this  value  of  Cc  find  by  means  of  (71)  several  values 
of  the  temperature  K^   of  the  pyrometer  lamp  corresponding  to 


126  OPTICAL  PYROMETRY 

values  of  K\.  Now  express  these  values  of  K*  on  the  centigrade 
scale  and  plot  them  against  the  current  i,  corresponding  to  the 
above  values  of  K*.  This  is  the  calibration  curve  of  the  instru- 
ment when  the  absorptive  glass  is  used. 

In  determining  temperatures  by  means  of  a  Holborn-Kurl- 
baum  Optical  Pyrometer  the  following  precautions  should  be 
heeded : 

(a)  The  sources  whose  temperatures  are  sought  should  be 
backgrounds  for  the  filament  of  the  comparison  lamp. 

(6)  A  single  comparison  lamp  should  be  used  throughout  a 
determination. 

(c)  The   angles  at  the   comparison   lamp   subtended   by   the 
aperture  of  the  objective  lens  and  by  the  aperture  of  the  eye 
lens  should  be  constant. 

(d)  The  apparatus  should  be  so  adjusted  that  there  is  axial 
symmetry. 

(e)  The  resolving  power  of  the  eyepiece  should  not  be  so  great 
as  not  to  permit  the  disappearance  of  the  tip  of  the  filament 
against  the  bright  background  image. 

(/)  The  image  of  the  background  should  be  large  in  comparison 
with  the  comparison  lamp  filament. 

Exp.  10.  Determination  of  the  Melting  Point  of  a  Very  Small 
Specimen  of  a  Substance 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  (40-43),  48.  The 
object  of  this  experiment  is  to  determine  the  melting  point  of  a 
specimen  no  larger  than  the  head  of  a  pin.  The  specimen  is 
placed  on  a  strip  of  sheet  platinum  which  can  be  heated  to  in- 
candescence by  an  electric  current.  When  the  platinum  strip 
attains  the  temperature  at  which  the  substance  melts,  the  edges 
of  the  specimen  will  become  rounded.  This  may  be  observed  by 
a  microscope.  The  temperature  of  the  strip  at  that  moment 
can  be  conveniently  obtained  by  means  of  a  Holborn-Kurlbaum 
pyrometer. 

Instead  of  using  a  microscope  and  separate  pyrometer,  one  can 


LUMINOUS  INTENSITY  AND  TEMPERATURE  127 

employ  a  single  microscope-pyrometer  which  consists  of  a  low 
power  compound  microscope  provided  with  a  small  incandescent 
lamp  in  the  focal  plane  of  the  ocular. 

The  result  of  the  observation  is  the  melting  point  K^  according 
to  the  absolute  black-body  temperature  scale.  From  this  value, 
the  thermodynamic  temperature  T  can  be  computed  from  the 
equation  (44), 

JL  _     1     i  ^  1°S a 
~T  =  Kx       6237   ' 

Where  a  is  the  absorptive  power  of  platinum  given  in  the  table 
at  the  end  of  Art.  41. 

The  manipulation  of  this  experiment  is  so  obvious  that  it  need 
not  be  here  elaborated. 

Exp.    11.  The    Determination    of   the    Relation   between   the 
Luminous  Intensity  and  the  Temperature  of  an  Incandes- 
cent Lamp  Filament 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  40,  42,  48,  and 
50.  The  luminous  intensity  of  any  body  emitting  light  due  to 
thermal  causes  increases  rapidly  with  increase  of  temperature. 
For  all  black-bodies  the  luminous  intensity  per  unit  area  at  a 
given  temperature  is  the  same.  But  at  a  given  temperature,  the 
luminous  intensities  of  various  nonblack-bodies  may  differ  within 
wide  limits.  It  is  therefore  important  to  know  the  luminous 
intensities  of  various  light  sources  at  different  temperatures. 
The  object  of  this  experiment  is  to  construct  a  curve  showing 
the  relation  between  the  luminous  intensity  and  the  black-body 
temperature  of  an  incandescent  lamp  filament. 

MANIPULATION.  —  This  experiment  requires  (a),  the  determi- 
nation of  the  temperatures  of  the  lamp  filament  when  operated 
with  various  currents,  and  (6),  the  determination  of  the  candle 
powers  of  the  lamp  filament  when  operated  with  various  currents. 

For  the  temperature  determination  the  Holborn-Kurlbaum 
method  is  best  suited.  The  pyrometer  employed  consists  of  a 
two  lens  astronomical  telescope,  OE,  Figs.  70  and  71,  with  a 


128 


OPTICAL  PYROMETRY 


small  8-volt  comparison  lamp,  C,  in  the  focal  plane  common  to 
the  two  lenses.  Approximately  monochromatic  light  is  produced 
by  means  of  a  red  filter  glass  between  the  comparison  lamp  and 
the  eye  of  the  observer. 


FIG.  70. 

In  Fig.  71,  the  standardized  pyrometer  lamp  P  and  ammeter  A 
are  shown  in  series  with  a  circuit  consisting  of  a  battery  B,  vari- 
able rheostat  R,  and  switch  S.  In  the  common  focal  plane  of 
the  objective  0  and  the  eyelens  E,  is  the  comparison  lamp  C. 


FIG.  71. 

This  is  connected  in  series  with  a  battery  B'}  ammeter  A',  vari- 
able rheostat  R',  and  switch  S'. 

Adjust  the  position  of  the  eyelens  relative  to  the  comparison 
lamp  till  a  sharp  image  of  the  tip  of  the  filament  is  seen  in  the 
center  of  the  field  of  view.  The  eyelens  and  comparison  lamp 


LUMINOUS  INTENSITY  AND  TEMPERATURE  129 

should  be  now  clamped  in  order  that  throughout  the  remainder 
of  the  experiment  their  position  may  be  unaltered. 

Adjust  the  position  of  the  pyrometer  lamp  and  objective  till 
an  image  of  the  pyrometer  lamp  ribbon  wider  than  the  comparison 
lamp  filament  is  formed  in  the  plane  of  the  comparison  lamp 
filament.  When  the  image  of  the  pyrometer  lamp  ribbon  is  in 
the  plane  of  the  comparison  lamp  filament,  there  will  appear  to 
be  no  motion  of  one  relative  to  the  other  on  moving  the  eye  to 
the  right  and  left  in  front  of  the  eyelens. 

Adjust  the  current  in  the  pyrometer  lamp  to  about  3  amperes. 
Adjust  the  current  in  the  comparison  lamp  till  the  tip  of  the 
filament  is  of  the  same  brightness  as  the  pyrometer  lamp  ribbon. 
Note  the  current  in  the  comparison  lamp  and  the  current  in  the 
pyrometer  lamp  ribbon.  Make  a  series  of  such  readings  at 
intervals  of  one  ampere  up  to  10  amperes.  From  these  data, 
construct  the  empirical  calibration  curve  coordinating  the  tem- 
perature of  the  pyrometer  ribbon  and  the  current  in  the  compar- 
ison lamp. 

From  three  points  on  this  empirical  curve,  not  less  than  300° 
apart,  compute  the  three  constants  in  (64).  By  means  of  the 
definite  equation  thereby  obtained,  compute  the  current  in  the 
comparison  lamp  corresponding  to  not  less  than  five  different 
temperatures  of  the  source  up  to  1700°  C.  Plot  these  computed 
values  on  the  sheet  with  the  empirical  curve.  A  curve  drawn 
through  these  points  should  closely  approximate  the  empirical 
curve.  The  pyrometer  is  now  calibrated  by  two  methods. 

Within  the  range  of  this  calibration,  the  temperatures  of  the 
incandescent  lamp  to  be  studied  can  now  be  determined.  Sub- 
stitute the  lamp  to  be  tested  for  the  pyrometer  lamp.  For  most 
commercial  lamps  the  electromotive  force  required  will  be  so 
much  greater  than  the  value  required  for  the  pyrometer  lamp 
that  the  lamp  to  be  tested  must  be  joined  in  series  with  a  storage 
battery  of  higher  electromotive  force.  Observe  a  series  of  values 
of  temperatures  and  currents  of  the  lamp  under  investigation  at 
intervals  of  0.05  ampere  from  0.3  ampere  to  normal  current. 
Plot  these  values  in  a  curve. 


130 


OPTICAL  PYROMETRY 


To  determine  the  candle  power  of  the  lamp  under  test  when 
operated  at  various  currents,  this  lamp  is  placed  at  one  end  of  a 
photometer  bar,  at  the  other  end  of  the  bar  is  placed  an  incan- 
descent lamp  for  which  the  candle  power  is  known  for  various 
current  values.  Each  lamp  is  in  series  with  a  storage  battery, 
variable  rheostat  and  ammeter,  Fig.  72. 

Adjust  the  current  in  the  test  lamp  to  the  value  corresponding 
to  a  temperature  of  700°  C.  Adjust  the  current  in  the  standard 


FIG.  72. 

lamp  till  the  colors  of  the  two  sources,  as  seen  on  the  pho- 
tometer screen  are  apparently  the  same.  Move  the  photometer 
screen  back  and  forth  till  the  two  halves  of  the  field  of  view  are 
equally  bright.  Note  the  reading  on  the  scale  of  the  photometer 
bar,  and  the  current  in  each  lamp. 

In  the  same  manner  take  a  series  of  readings,  at  0.05-ampere 
intervals,  up  to  the  normal  current. 

The  candle  power  of  the  standard  is  obtainable  from  the  pre- 
viously obtained  " current-candle  power"  calibration  curve.  The 
candle  power  of  the  test  lamp  is  computed  by  means  of  the  ordi- 
nary law  of  photometry,  7  2 

(72) 


where  I\  and  Iz  represent  the  luminous  intensities  of  the  two 
lamps  and  r\  and  rz  the  distances  from  the  photometer  screen 


CALIBRATION  OF  A  F^RY  ABSORPTION  PYROMETER      131 

to  the  two  lamps,  respectively,  when  the  two  halves  of  the  screen 
are  equally  bright. 

Tabulate  the  data  obtained  from  this  part  of  the  experiment 
as  follows: 


In  this  table  it  represents  the  current  operating  the  test  lamp; 
rtj  the  distance  of  the  photometer  screen  from  the  test  lamp  when 
both  halves  of  the  screen  are  equally  bright;  It,  the  candle  power 
of  the  test  lamp;  t,  the  centigrade  temperature  of  the  test  lamp. 
Similar  quantities  referring  to  the  standard  lamp  are  designated 
by  the  subscript  s.  The  quantities  in  the  last  column  are  obtain- 
able from  the  "  temperature-current  "  curve  previously  constructed. 

With  the  data  in  the  last  two  columns  construct  the  curve 
coordinating  the  candle  power  and  the  temperature  of  the  lamp 
under  investigation. 

Exp.  12.   Calibration  of  a  Fery  Absorption  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  (39-42),  46.  For 
a  description  of  the  instrument  see  Art.  46.  Denote  the  ab- 
sorption per  unit  thickness  of  the  glass  composing  the  wedges  by 
the  symbol  a,  the  thickness  of  the  part  of  the  wedges  traversed 
by  light  from  the  source  by  the  symbol  xt  the  rate  with  which 
energy  of  wave-length  X  is  incident  on  the  objective  by  the  sym- 
bol Jx,  and  the  rate  with  which  energy  of  wave-length  X  emerges 
from  the  absorbing  wedges  by  J\.  Then  we  may  write: 

Jx  =  aVx'. 

Representing  by  7X  the  rate  with  which  radiance  of  wave-length 
X  leaves  unit  area  of  the  source,  we  may  write  when  the  objective 
subtends  at  the  image  a  constant  angle, 


where  z  is  a  constant  of  proportionality. 


132  OPTICAL  PYROMETER 

Whence  7X  =  (a/xO  a*  =  ba*, 

where  6  represents  the  constant  quantity  within  the  parenthesis. 
If  Wien's  Distribution  Law  (39)  is  applicable, 


log/x[ 


i  -         =  Iog6  +  a;  log  a, 

/d-logftX      g_ 
I     log  a     J          ~ 


log  a  ~oga_' 

which  may  be  put  into  the  form 

d 

c-x  =  —> 
AX 

where  c  represents  the  constant  quantity  within  the  parenthesis 
and  d  the  quantity  within  the  bracket.  Clearing  of  fractions 
and  changing  signs,  the  relation  between  x  and  K\  when  there 
is  no  absorptive  glass  in  front  of  the  wedges  is  seen  to  be  : 

K*  (z  -  c)  =  -d.  (73) 

The  two  constants  in  this  equation  can  be  determined  if  the 
wedge  thickness  x,  corresponding  to  two  absolute  temperatures 
are  known.  From  the  definite  equation  thereby  obtained,  we 
can  compute  values  of  K\  corresponding  to  a  series  of  values 
of  Xj  and  from  these  values  of  K\  and  x  construct  the  calibration 
curve  of  the  instrument  when  no  absorptive  glass  is  in  front  of 
the  wedges. 

With  the  absorptive  glass  No.  1  in  front  of  the  wedges,  the 
corresponding  formula  is 

#x  (x  -  c  +  n)  =  -d,  (74) 

and  with  absorptive  glasses  Nos.  1  and  2  in  front  of  the  wedges, 
the  corresponding  formula  is 

#x  (x  -  c  +  n  +  r2)  =  -d.  (75) 

For  the  solution  of  (74)  values  of  x  corresponding  to  three 
known  temperatures  must  be  obtained.  And  for  the  solution  of 
(75)  values  of  x  corresponding  to  four  known  temperatures  must 
be  obtained. 


COLOR  IDENTITY  OPTICAL  PYROMETER  133 

The  object  of  this  experiment  is  to  construct  the  calibration 
curve  of  a  Fe"ry  Absorption  Pyrometer  with  no  absorptive  glass 
in  front  of  the  wedges.  This  curve  is  to  be  obtained  by  the 
step-by-step  method  and  also  by  computation  from  two  experi- 
mentally determined  points. 

MANIPULATION.  —  The  lamp  is  to  be  filled  with  pure  amyl 
acetate  and  the  flame  allowed  to  burn  for  a  few  minutes  before 
beginning  observations.  The  wick  is  to  be  adjusted  so  that  the 
tip  of  the  flame  is  maintained  at  the  top  of  the  slit  in  the  chimney. 
Adjust  the  eyepiece  of  the  telescope  till  the  illuminated  oval 
patch  of  light  due  to  the  lamp  is  distinct.  By  means  of  the 
rack  and  pinion  focalize  the  telescope  on  the  septum  within  a 
"black-body."  See  that  the  red  glass  filter  is  in  place  in  the 
eyepiece.  If  the  various  glass  surfaces  are  not  free  of  dirt  and 
moisture  they  are  to  be  carefully  cleaned. 

Beginning  when  the  " black-body"  is  at  about  900°  C.  take  a 
series  of  readings  at  25°  intervals,  of  the  wedge  thickness  required 
to  bring  the  two  parts  of  the  field  of  view  to  equal  brightness. 
From  these  readings  construct  the  empirical  step-by-step  cali- 
bration curve  of  the  instrument. 

From  the  coordinates  of  two  points  of  this  curve,  as  far  apart 
as  convenient,  compute  the  constants  in  (73). 

Substitute  in  the  definite  equation  thereby  obtained,  x  =  0, 
x  =  10,  x  =  20,  etc.,  x  =  90,  and  compute  the  corresponding 
values  of  K\. 

On  the  same  sheet  with  the  step-by-step  calibration  curve, 
construct  the  calibration  curve  obtained  from  these  values. 

Exp.  13.   Calibration  of  a  Color  Identity  Optical  Pyrometer 

THEORY  OF  THE  EXPERIMENT.  —  Read  Art.  44.  The  Color 
Identity  Method  of  measuring  temperatures  depends  upon  the 
fact  that  black  or  gray  bodies  are  at  the  same  thermodynamic 
temperature  when  the  light  radiated  from  them  is  of  the  same 
color.  The  method  requires,  (a)  a  comparison  source  of  known 
temperature  that  can  be  varied  within  wide  limits,  (6)  some 


134  OPTICAL  PYROMETRY 

means  by  which  a  spot  of  light  from  the  source  whose  temperature 
is  sought  and  one  from  the  comparison  source  can  be  brought 
to  equal  brightness,  (c)  a  device  that  will  give  sharp  indications 
of  small  color  differences. 

The  most  satisfactory  comparison  source  is  a  wide  carbon 
filament  incandescent  lamp.  The  relation  between  the  current 
i  and  the  thermodynamic  temperature  t,  expressed  according 
to  the  centigrade  scale,  is  given  by  (64) 

i  =  a  +  bt  +  d2,  (640 

where  a,  6,  and  c  are  three  constants  for  a  particular  filament, 
but  different  for  different  filaments. 

In  the  instrument  designed  in  Purdue  University,  Fig.  73,  light 
from  the  source  whose  temperature  is  sought  is  reduced  to  the 

brightness  of  light  from  the 
comparison  source  L,  by  means 
of  two  Nicol  prisms  P  and  A. 
The  color  of  light  from  the  two 
sources  is  compared  by  means 
of  a  Lummer-Brodhun  photom- 
eter screen  B.  This  consists  of 
two  right-angled  prisms  x  and 
y,  Fig.  73.  The  hypothenuse 

face  of  each  prism  is  ground  to  opacity  except  for  a  central 
polished  round  spot.  The  transparent  spot  on  x  is  smaller  than 
that  on  y.  Light  from  the  left  incident  upon  the  small  polished 
spot  will  be  transmitted,  whereas  that  incident  on  the  ground 
portion  of  the  hypothenuse  face  will  be  reflected  to  one  side. 
Light  from  below  incident  on  the  central  part  of  the  hypothenuse 
face  of  y  will  go  through  both  prisms,  whereas  that  incident  be- 
tween the  edge  of  the  small  spot  and  the  edge  of  the  large  spot 
will  be  reflected  to  the  right.  On  looking  through  the  eyepiece 
focalized  on  the  center  of  the  hypothenuse  faces,  one  sees  a  cen- 
tral round  patch  of  light  from  the  source  whose  temperature  is 
sought,  surrounded  by  a  ring  of  light  from  the  comparison  source. 
When  the  two  patches  are  equally  bright,  small  differences  of 
color  are  readily  distinguished. 


ACTUAL  TEMPERATURES  OF  A  GRAY  BODY          135 

MANIPULATION.  —  Direct  the  instrument  into  a  "  black-body" 
provided  with  a  standardized  thermoelectric  pyrometer.  In  order 
to  exclude  extraneous  light  a  tube  blackened  on  the  inside  should 
connect  the  pyrometer  and  the  end  of  the  "black-body."  Rotate 
one  of  the  Nicol  prisms  and  adjust  the  current  in  the  comparison 
lamp  till  the  two  parts  of  the  field  of  view  are  equally  bright  and 
of  the  same  color.  Note  the  current  in  the  comparison  lamp  and 
the  temperature  of  the  "  black-body."  In  the  same  manner  take 
readings  of  the  current  for  a  series  of  temperatures  at  100°  inter- 
vals throughout  the  range  of  the  "  black-body."  With  tempera- 
tures as  abscissas  and  currents  as  ordinates,  plot  the  step-by-step 
calibration  curve  of  the  instrument. 

From  the  coordinates  of  three  points  of  this  curve  as  far  apart 
as  convenient,  compute  the  constants  in  (64'),  and  write  the 
definite  equation  of  the  calibration  curve.  By  substituting  in 
this  equation  various  convenient  values  for  t,  compute  a  series 
of  values  of  i.  On  the  same  sheet  with  the  empirical  curve,  plot 
this  computed  curve. 

After  the  color  identity  optical  pyrometer  has  been  calibrated, 
it  can  be  used  to  measure  thermodynamic  temperatures  of  gray 
as  well  as  of  black-bodies.  The  equality  of  brightness  optical 
pyrometer  as  well  as  all  radiation  pyrometers  indicate  thermo- 
dynamic temperatures  of  black-bodies  only. 

Exp.  14.  The  Measurement  of  Actual  Temperatures  of  a  Gray 

Body 

THEORY  OF  THE  EXPERIMENT.  —  Read  Arts.  40,  49  and  Theory 
of  Exp.  8.  A  gray  body  has  been  defined  as  one  which  radiates 
with  constant  emissive  power  for  all  wave-lengths.  Then  if  the 
energy  of  wave-length  X,  radiated  by  a  black-body  at  absolute 
thermodynamic  temperature  T,  is  given  by  Wien's  Law  (37), 


/A  = 

the  energy  of  wave-length  X  radiated  by  a  gray  body  at  the  same 
temperature  is  _CL  _c*_ 

XT 


136  OPTICAL  PYROMETRY 

where  a  is  the  emissive  power  which  is  constant  for  all  values  of 
X  and  K  is  the  black-body  temperature  of  the  gray  body. 

Putting  these  equations  in  the  logarithmic  form  we  get  (Art.  40), 

logIx-Ci-|*,  (76) 

log  7X'  =  log  a  +  Ci  -  §  =  C,  -  %•  (77) 

1  J\. 

Let  the  gray  body  be  kept  at  a  constant  temperature  and  be 
used  as  the  comparison  source  in  a  Wanner  Optical  Pyrometer. 
Also  let  the  radiation  from  a  black-body  at  various  temperatures 
and  of  various  wave-lengths  be  compared  with  that  of  the  gray 
body  kept  at  constant  temperature. 

Then  for  any  wave-length  X  (60), 

£=tan«0  (78) 

•/x 

where  9  is  the  angle  read  from  the  instrument.    This  in  loga- 
rithmic form  is 

log  7X  =  log  /A'  +  log  tan2  0  =  C"  +  log  tan2  0. 
If  this  value  of  log  7\  be  substituted  in  (76),  we  have 

log  tan2  B  =  Ci-C"-|;2> 
or,  log  tan2  6  =  C.-ft.!. 

This  equation  shows  that  the  relation  between  the  reciprocal 
of  the  absolute  thermodynamic  temperature  of  the  black-body 
and  the  reading  of  the  instrument  is  linear,  and  when  plotted 
will  give  a  straight  line.  Also  since  (78), 


±i    =-   =tan20, 
/A  L     aJ 

when  the  black-body  and  the  gray  body  are  at  the  same  tem- 
perature, the  curves  coordinating  -  and  log  tan20  for  various 


ACTUAL  TEMPERATURES  OF  A  GRAY  BODY  137 

wave-lengths  must  pass  through  a  common  point.     The  coordi- 
nate —  of  this  point  gives  the  actual  temperature  of  the  gray  body. 

If  the  comparison  body  does  not  radiate  as  a  gray  body  the 
curves  may  not  meet  in  a  common  point  and  its  actual  tempera- 
ture cannot  be  determined  in  this  way. 

From  (77),  log  a  =  C2(|  -  - 

,  6297 

or,  since  (40)  C2  =  -  » 

X 

6297/1 

logo=—   -  (79) 


Again,  if  we  measure  the  black-body  temperature  of  the  gray 
body,  and  have  the  actual  temperature  by  the  method  outlined 
above,  (79)  gives  a  means  of  determining  the  emissive  power  of 
the  gray  body. 

There  are  many  substances  which  radiate  as  gray  bodies  within 
the  visible  portion  of  the  spectrum  and  within  certain  tempera- 
ture ranges.  The  materials  used  as  filaments  of  some  incan- 
descent lamps  are  among  these.  The  object  of  this  experiment 
is  to  determine  actual  temperatures  of  the  filament  of  an  incan- 
descent lamp  for  various  current  values. 

MANIPULATION.  —  In  some  Wanner  Optical  Pyrometers  used 
for  rather  low  temperatures,  approximately  monochromatic  light 
is  obtained  by  the  use  of  a  collimating  lens  of  red  glass  instead 
of  by  the  use  of  the  prism.  If  this  red  glass  lens  be  replaced  by 
one  of  clear  glass,  the  instrument  will  be  adapted  to  making 
the  measurements  required  in  this  experiment.  Monochromatic 
light  may  be  obtained  by  the  use  of  colored  filter  glasses. 

Heat  a  tube  furnace  which  is  to  serve  as  a  "black-body"  until 
the  temperature  has  become  constant.  The  temperature  of  the 
"black-body"  must  be  determined  by  means  of  a  standard  ther- 
mocouple or  other  means.  Direct  the  Wanner  pyrometer  toward 
the  furnace.  Set  the  current  in  the  comparison  lamp  at  some 


138  OPTICAL  PYROMETRY 

convenient  value  and  read  the  position  of  the  pointer  when  the 
analyzer  is  set  for  equal  brightness,  using  in  turn  at  least  three 
differently  colored  filter  glasses. 

Repeat  this  for  several  different  values  of  current  through  the 
comparison  lamp,  keeping  the  temperature  of  the  " black-body" 
constant. 

Then  change  the  temperature  of  the  "black-body"  to  some 
other  constant  value,  and  take  another  series  of  readings  for  the 
same  series  of,  current  values  above. 

Repeat  for  a  third  temperature  of  the  "black-body." 

Plot  the  curves  between  —  and  log  tan2  6  and  obtain  the  values 

of  the  actual  temperatures  of  the  comparison  lamp  filament  for 
the  various  currents. 

Plot  a  curve  between  actual  temperatures  of  the  lamp  and 
current  through  it. 

It  is  not  necessary  to  use  a  "black-body"  for  every  measure- 
ment. The  "black-body"  can  be  replaced  by  an  incandescent 
lamp  which  radiates  as  a  gray  body,  if  the  curve  between  current 
and  actual  thermodynamic  temperature  is  known  for  this  lamp. 
Thus,  the  lamp  used  as  a  comparison  lamp  in  the  Wanner  pyrom- 
eter could  be  calibrated  by  comparison  with  a  "black-body" 
and  then  used  instead  of  the  "black-body"  in  subsequent  meas- 
urements. When  thus  calibrated,  the  Wanner  pyrometer  may 
be  used  for  measuring  actual  temperatures  of  gray  bodies.  In 
this  case  the  complement  of  the  angle  read  on  the  instrument 
must  be  taken. 

CONCLUSION 

51.  The  Selection  of  Pyrometers  for  Particular  Purposes.  — 

Of  all  temperature-measuring  instruments  the  mercury-in-glass 
thermometer  is  the  simplest  to  use  and  is  employed  wherever 
possible.  When  the  tube  above  the  mercury  is  filled  with  a  gas 
under  pressure  to  prevent  boiling  of  the  mercury,  such  ther- 
mometers can  be  used  up  to  550°  C.  The  instrument  is  subject 
to  variation  when  used  long  at  the  higher  temperatures  and 


PYROMETERS  FOR  PARTICULAR  PURPOSES  139 

should  be  occasionally  checked  against  known  melting  points. 
The  indications  give  thermodynamic  or  real  temperatures. 

Second  only  to  the  mercury-in-glass  thermometer,  the  thermo- 
electric pyrometer  is  most  often  used.  The  base  metal  thermo- 
electric pyrometer  is  available  for  temperatures  up  to  about 
1200°  C.,  and  the  rhodioplatinum  thermoelectric  for  short  inter- 
vals of  time  up  to  1500°  C.  Thermoelectric  pyrometers  can  be 
used  in  connection  with  recorders.  The  indications  give  thermo- 
dynamic or  real  temperatures. 

The  resistance  pyrometer  is  available  for  temperatures  up  to 
900°  C.  and  is  capable  of  greater  precision  than  any  other  pyrom- 
eter. It  indicates  real  temperatures  and  can  be  used  in  connec- 
tion with  recorders.  It  is  not  so  robust  and  is  not  so  simple 
to  use  as  the  thermoelectric  pyrometer. 

There  is  no  limit  to  the  upper  temperature  for  which  radiation 
and  optical  pyrometers  can  be  employed.  The  lower  limit  is 
different  for  different  types  of  instrument.  When  the  body 
whose  temperature  is  sought  is  within  a  uniformly  heated  en- 
closure, the  indications  of  a  radiation  or  an  optical  pyrometer 
represent  true  temperatures;  otherwise,  the  indications  give  not 
real  temperatures,  but  black-body  temperatures.  Unless  the 
emissivity  of  the  surface  of  the  hot  body  is  known,  it  is  impossible 
to  translate  black-body  or  apparent  temperatures  into  thermo- 
dynamic or  real  temperatures.  For  this  reason,  radiation  and 
optical  pyrometers  are  used  only  when  the  instrument  depending 
upon  other  principles  cannot  be  employed.  But  where  the  body 
whose  temperature  is  sought  is  inaccessible  or  too  high  in  tem- 
perature for  the  other  methods,  recourse  must  be  had  to  radiation 
or  optical  methods. 

The  Thwing  and  Foster  radiation  pyrometers  can  be  used  as 
low  as  400°  C.,  and  the  Fe"ry  Mirror  Radiation  Pyrometer  as  low 
as  500°  C.  These  instruments  can  be  used  in  connection  with 
recorders. 

Optical  pyrometers  employing  a  flame  for  the  comparison  light 
source  are  unsuited  to  places  where  there  are  drafts  or  air  cur* 
rents.  The  Wanner  optical  pyrometer  as  well  as  the  Morse  or 


140  OPTICAL  PYROMETRY 

Holborn-Kurlbaum  optical  pyrometer  can  be  used  from  700°  C. 
up^  The  Holborn-Kurlbaum  instrument  has  certain  advantages 
over  the  Wanner  in  that  by  it  the  temperature  of  smaller  bodies 
can  be  determined,  and  the  settings  more  easily  made.  When 
both  can  be  used  equally  well,  there  is  no  choice  as  to  precision. 
The  use  of  optical  pyrometers  requires  the  making  of  a  setting 
involving  a  judgment.  The  indication  of  a  radiation  pyrometer 
is  read  directly  from  a  millivoltmeter.  In  the  hands  of  a  careful 
observer,  an  optical  pyrometer  is  capable  of  greater  precision 
than  a  radiation  pyrometer,  but  a  person  of  no  training  can  get 
better  results  with  a  radiation  pyrometer  than  with  an  optical 
pyrometer. 


BOILING  WATER  UNDER  BAROMETRIC  PRESSURES     141 


TABLE  1.  — Boiling  Point  of  Water  under  Different 
Barometric  Pressures 

(a)  Temperatures  in  Degrees  Centigrade  and  Pressures  in  Millimeters  of 

Mercury 


o  /-^ 

<^. 

'7 

90 

525.4 

527.4 

529.4 

531.4 

533.4 

535.5 

537.5 

539.6 

541.6 

543.7 

91 

545.7 

547.8 

549.9 

551.9 

554.0 

556.1 

558.2 

560.3 

562.4 

564.6 

92 

566.7 

568.8 

571.0 

573.1 

575.3 

577.4 

579.6 

581.8 

584.0 

586.1 

93 

588.3 

590.5 

592.7 

595.0 

597.2 

599.4 

601.6 

603.9 

606.1 

608.4 

94 

610.7 

612.9 

615.2 

617.5 

619.8 

622.1 

624.4 

626.7 

629.0 

631.4 

95 

633.7 

636.0 

638.4 

640.7 

643.1 

645.5 

647.9 

650.2 

652.6 

655.0 

96 

657.4 

659.9 

662.3 

664.7 

667.1 

669.6 

672.0 

674.5 

677.0 

679.4 

97 

681.9 

684.4 

686.9 

689.4 

691.9 

694.5 

697.0 

699.5 

702.1 

704.6 

98 

707.2 

709.7 

712.3 

714.9 

717.5 

720.1 

722.7 

725.3 

727.9 

730.5 

99 

733.2 

735.8 

738.5 

741.2 

743.8 

746.5 

749.2 

751.9 

754.6 

757.3 

100 

760.0 

762.7 

765.5 

768.2 

770.9 

773.7 

776.5 

779.2 

782.0 

784.8 

(b)  Temperatures  in  Degrees  Fahrenheit  and  Pressures  in  Inches  of  Mercury 


°F. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

,.8 

.9 

194 

20.68 

20.73 

20.77 

20.82 

20.86 

20.90 

20.95 

20.99 

21.04 

21.08 

195 

21.13 

21.17 

21.22 

21.26 

21.30 

21.35 

21.39 

21.44 

21.48 

21.53 

196 

21.58 

21.62 

21.67 

21.71 

21.76 

21.80 

21.85 

21.89 

21.94 

21.99 

197 

22.03 

22.08 

22.12 

22.17 

22.22 

22.26 

22.31 

22.36 

22.40 

22.45 

198 

22.50 

22.54 

22.59 

22.64 

22.69 

22.73 

22.78 

22.83 

22.88 

22.92 

199 

22.97 

23.02 

23.07 

23.11 

23.16 

23.21 

23.26 

23.31 

23.36 

23.40 

200 

23.45 

23.50 

23.55 

23.60 

23.65 

23.70 

23.75 

23.80 

23.85 

23.89 

201 

23.94 

23.99 

24.04 

24.09 

24.14 

24.19 

24.24 

24.29 

24.34 

24.39 

202 

24.44 

24.49 

24.54 

24.59 

24.64 

24.69 

24.74 

24.80 

24.85 

24.90 

203 

24.95 

25.00 

25.05 

25.10 

25.15 

25.21 

25.26 

25.31 

25.36 

25.41 

204 

25.46 

25.52 

25.57 

25.62 

25.67 

25.73 

25.78 

25.83 

25.88 

25.94 

205 

25.99 

26.04 

26.10 

26.15 

26.20 

26.25 

26.31 

26.36 

26.42 

26.47 

206 

26.52 

26.58 

26.63 

26.68 

26.74 

26.79 

26.85 

26.90 

26.96 

27.01 

207 

27.07 

27.12 

27.18 

27.23 

27.29 

27.34 

27.40 

27.45 

27.51 

27.56 

208 

27.62 

27.67 

27.73 

27.79 

27.84 

27.90 

27.95 

28.01 

28.07 

28.12 

209 

28.18 

28.24 

28.29 

28.35 

28.41 

28.46 

28.52 

28.58 

28.64 

28.69 

210 

28.75 

28.81 

28.87 

28.92 

28.98 

29.04 

29.10 

29.16 

29.21 

29.27 

211 

29.33 

29.39 

29.45 

29.51 

29.57 

29.62 

29.68 

29.74 

29.80 

29.86 

212 

29.92 

29.98 

30.04 

30.10 

30  16 

30.22 

30.28 

30.34 

30.40 

30.46 

142 


BAROMETER  CORRECTIONS 


TABLE  2.  —  Corrections  for  the  Influence  of  Gravity  on  the 
Height  of  the  Barometer 

(a)  Reduction  to  Latitude  45° 

^From  0°  to  45°  the  corrections  are  subtractive;  from  45°  to  90°  the  cor- 
rections are  additive. 


T  at 

Barometric  height  in  mm.  reduced  to  0°  C. 

.Lat. 

670 

680 

690 

700 

710 

720 

730 

740 

750 

760 

770 

780 

Lat. 

Dy 

mm. 

.74 

mm. 

1.76 

mm. 

1.79 

mm. 
1.81 

mm. 
1.84 

mm. 

1.86 

mm. 

1.89 

mm. 

1.92 

mm. 
1.94 

mm. 

1.97 

mm. 
1.99 

mm. 
2.02 

Deg. 
90 

5 

.71 

1.73 

1.76 

1.79 

1.81 

1.84 

1.86 

1.89 

1.91 

1.94 

1.96 

1.99 

85 

10 

.63 

1.65 

1.68 

•1.70 

1.73 

1.75 

1.78 

1.80 

1.83 

1.85 

1.87 

1.90 

80 

15 

.50 

1.53 

1.55 

1.57 

1.59 

1.61 

1.64 

1.66 

1.68 

1.70 

1.73 

1.75 

75 

20 

.33 

1.35 

1.37 

1.39 

1.41 

1.43 

1.45 

1.47 

1.49 

1.51 

1.53 

1.55 

70 

25 

1.12 

1.13 

1.15 

1.17 

1.18 

1.20 

1.22 

1.23 

1.25 

1.27 

1.28 

1.30 

65 

30 

0.87 

0.88 

0.89 

0.91 

0.92 

0.93 

0.95 

0.96 

0.97 

0.98 

0.00 

0.01 

60 

35 

0.59 

0.60 

0.61 

0.62 

0.63 

0.64 

0.65 

0.66 

0.66 

0.67 

0.68 

0.69 

55 

40 

0.30 

0.31 

0.31 

0.31 

0.32 

0:32 

0.33 

0.33 

0.34 

0.34 

0.35 

0.35 

50 

45 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

0.00 

45 

(b)  Reduction  to  Sea  Level 
Corrections  are  subtractive. 


Barometric  height  in  mm.  reduced  to  0°  C. 


Hiievauon. 

660 

680 

700 

720 

740 

760 

770 

m. 

100 

mm. 

mm. 

mm. 

0.01 

mm. 

0.01 

mm. 

0.01 

mm. 

0.01 

mm. 

0.02 

200 

0.03 

0.03 

0.03 

0.03 

0.03 

0.03 

300 

0.04 

0.04 

0.04 

0.04 

0.04 

400 

0.05 

0.05 

0.05 

0.06 

0.06 

0.06 

500 

0.06 

0.07 

0.07 

0.07 

0.07 

0.07 

600 

0.08 

0.08 

0.08 

0.08 

0.09 

700 

0.09 

0.09 

0.10 

0.10 

0.10 

800 

0.10 

0.11 

0.11 

0.11 

0.12 

900 

0.12 

0.12 

0.12 

0.13 

1000 

0.13 

0.13 

0.14 

0.14 

WANNER  OPTICAL  PYROMETER 


143 


TABLE  3.  — Values  of  log  (tan2  6)  for  Use  with  the  Wanner 
Optical  Pyrometer 


e 

log  (tan*  6) 

e 

log  (tan*  6) 

e 

log  (tan*  8) 

Deg. 

Deg. 

Deg. 

10 

-1.50736 

34 

-0.34202 

58 

0.40842 

11 

-  .42270 

35 

-0.30954 

59 

0.44246 

12 

-  .34506 

36 

-0.27748 

60 

0.47712 

13 

-  .27328 

37 

-0.24578 

61 

0.51250 

14 

-  .20646 

38 

-0.21438 

62 

0.54866 

15 

-  .14390 

39 

-0.18326 

63 

0.58566 

16 

-  .08500 

40 

-0.15238 

64 

0.62364 

17 

-  .02932 

41 

-0.12168 

65 

0.66266 

18 

-0.97642 

42 

-0.09112 

66 

0.70284 

19 

-0.92606 

43 

-0.06068 

67 

0.74430 

20 

-0.87786 

44 

-0.03032 

68 

0.78718 

21 

-0.83164 

45 

0.00000 

69 

0.83164 

22 

-0.78718 

46 

0.03032 

70 

0.87786 

23 

-0.74430 

47 

0.06068 

71 

0.92606 

24 

-0.70284 

48 

0.09112 

72 

0.97642 

25 

-0.66266 

49 

0.12168 

73 

1.02932 

26 

-0.62364 

50 

0.15238 

74 

.08500 

27 

-0.58566 

51 

0.18326 

75 

.14390 

28 

-0.54866 

52 

0.21438 

76 

.20646 

29 

-0.51250 

53 

0.24578 

77 

.27328 

30 

-0.47712 

54 

0.27748 

78 

.34506 

31 

-0.44246 

55 

0.30954 

79 

1.42270 

32 

-0.40842 

56 

0.34202 

80 

1.50736 

33 

-0.37496 

57 

0.37496 

INDEX 


Absolute  zero,  5. 
Absorptive  power,  89. 
Antimony,  melting  point  of,  59. 

Barium  chloride,  melting  point  of,  59. 
Base  metal  thermocouples,  28. 
Benzophenone,  boiling  point  of,  20. 
Bismuth,  melting  point  of,  59. 
Black  body,  definition  of,  8. 
Black  body,  experimental,  71. 
Black  body  temperature  scale,  8. 
Black    body    temperature    of    non- 
black  bodies,  11. 
Boiling  points,  20. 
Box  bridges,  13,  14. 
Bridge,  Wheatstone,  12. 

Centigrade  scale,  3. 

Cold-junction  correction,  40. 

Cold-junction  errors,  reduction  of,  51. 

Color  identity  method,  100. 

Color  identity  pyrometer,  133. 

Comparison  of  various  pyrometers, 
138. 

Compensating  Wheatstone  bridge,  54. 

Compensator  thermocouple,  52. 

Construction  of  thermocouples,  28, 
62. 

Copper,  melting  point  of,  59. 

Corrections  for  hydrogen  tempera- 
ture scale,  8. 

Corrections  for  nitrogen  temperature 
scale,  8. 

Correction  for  cold-junction  tem- 
perature, 40,  43,  49. 

Critical  points,  67. 


Decalescent  point,  67. 
Deflection  potentiometer,  35. 

Emissive  power,  89. 

Fahrenheit  scale,  3. 

Fe*ry  absorption  pyrometer,  102. 

calibration  of,  131. 
Fe>y  mirror  radiation  pyrometer,  75. 
F4ry  spiral  pyrometer,  79. 
Fixed  points  of  temperature  scale,  3. 
Furnaces,  electric,  72. 

Gas,  ideal,  5. 

Gases,  fundamental  law  of,  5. 
Gray  body,  definition  of,  100. 
Gray   body,    determination   of    the 
temperature  of,  135. 

Holborn-Kurlbaum  optical  pyrome- 
ter, 104. 

Holborn-Kurlbaum  pyrometer,  cali- 
bration of,  122. 

Hydrogen  temperature  scale,  7. 

Ideal  gas  temperature  scale,  5. 
Indicators,  thermoelectric,  29. 

millivoltmeter,  29. 

potentiometer,  31,  34. 
Installation  of  thermocouples,  56. 
Inversion,  thermoelectric,  25. 

Kirchhoff's  law,  89. 


Lamp,  wide  filament  pyrometer,  107. 
Law  of  gases,  5. 


1*5 


146 


INDEX 


Law,  Kirchhoff's,  89. 

Planck's,  90. 

Stefan-Boltzmann,  8. 

Wien's  distribution,  90. 
Lead,  melting  point  of,  59. 
Le  Chatelier's  optical  pyrometer,  100. 
calibration  of,  108. 

Melting  points,  59. 

determination    of    by    thermo- 
couple, 60. 
of  small  pieces,  determination  of, 

126. 
Millivoltmeter  indicators,  29. 

resistance  of,  30. 
Morse  thermogauge,  104. 

Naphthalene,  boiling  point  of,  20. 
Neutral  temperature,  25. 
Nickel,  melting  point  of,  59. 
Nitrogen  temperature  scale,  7. 
Normal  point  of  Wanner  pyrometer, 

121. 

N  ormal  thermometer,  6. 
Northrup  pyrovolter,  38. 

Optical  pyrometry,  89. 
Optical  pyrometer  equation,  97. 

Parasitic  currents,  27. 
Perfect  gas,  5. 
Planck's  law,  90. 
Potentiometer,  deflection,  35. 
Potentiometer  indicators,  31,  34. 
Pyrometer,  Brown  radiation,  82. 

direct  reading  resistance,  14. 

Fe"ry  absorption,  102. 

Fe*ry  mirror,  75. 

Fe*ry  spiral,  79. 

fixed  focus  radiation,  80. 

Foster  radiation,  81. 

Holborn-Kurlbaum,  104. 

Le  Chatelier  optical,  100. 

recording  resistance,  16. 

recording  thermoelectric,  39. 


Pyrometer  (continued): 

resistance,  12. 

thermoelectric,  26. 

Thwing  radiation,  82. 

Wanner,  105. 
Pyroscope,  Shore,  103. 
Pyrovolter,  Northrup,  38.         • 

Radiation  pyrometry,  73. 

Recalescent  point,  68. 

Recording  resistance  pyrometer,  16. 

Recording  thermoelectric  pyrometer, 
39. 

Resistance  and  temperature,  12. 

Resistance,  measurement  of,  12. 

Resistance  of  millivoltmeter  indi- 
cators, 30. 

Resistance  pyrometers,  14. 

Salt,  melting  point  of,  59. 
Seebeck  effect,  24. 
Shore  pyroscope,  103. 
Silver,  melting  point  of,  59. 
Stefan-Boltzmann  law,  8. 
Sulphur,  boiling  point  of,  20. 

Temperature,  comparison  of,  1. 

black  body,  80. 

Centigrade,  3. 

Fahrenheit,  3. 

neutral,  25. 

scales,  2. 

scale,  ideal  gas,  5. 

thermodynamic,  4. 
Thermocouple,  25. 

base  metal,  28. 

compensating,  52. 

construction  of,  28,  62. 
Thermoelectric  indicators,  29. 

power,  27. 

pyrometer,  26. 
calibration  of,  58. 
installation  of,  56. 

inversion,  25. 


INDEX 


147 


Thermoelectromotive  force,  24. 
Thermometer,  normal,  6. 
Tin,  melting  point  of,  59. 
Transformation  points,  67. 

Wanner  optical  pyrometer,  105. 
calibration  of,  114. 


Wheatstone  bridge,  12. 
compensating,  54. 

Wide  filament  pyrometer  lamp,  107. 
Wien's  distribution  law,  90. 

Zero,  absolute,  5. 

Zinc,  melting  point  of,  59. 


Third  Edition,  Rewritten  and  Enlarged 


THE  MEASUREMENT  OF  HIGH 
TEMPERATURES 

BY 
G.  K.  BURGESS,  Bureau  of  Standards 

AND 

H.  LE  CHATELIER,  Membre  de  VInstitut 

This  book  gives  to  the  reader  the  history  and  origin  of  the 
pyrometer.  Several  types  of  this  instrument  have  been  dis- 
cussed, giving  in  detail  their  use  and  manufacture. 

This  volume.  —  It  is  practical  in  its  application  to  the  en- 
gineer in  his  efforts  to  adapt  some  method  or  instrument  to  a 
particular  technical  operation,  and  will  also  prove  valuable 
to  the  investigator  who  is  interested  in  accurate  methods  of 
measurement  and  their  adaptability  to  his  needs. 
-  In  reviewing  this  book  the  Metallurgical  and  Chemical  En- 


"The  book  is  really  monumental,  and  tfce  technical  world 
may  congratulate  itself  on  having  such  a  treatise." 

TABLE  OF  CONTENTS 

Introduction.  Standard  Scale  of  Temperatures.  Gas  Py- 
rometer. Calorimetric  Pyrometry.  Thermoelectric  Pyrometer. 
Electrical  Resistance  Pyrometer.  The  Laws  of  Radiation. 
Radiation  Pyrometer.  Optical  Pyrometer.  Various  Pyrometric 
Methods.  Recording  Pyrometers.  Standardization  of  Pyrom- 
eters. Bibliography.  Appendix:  Tables.  Index. 

xviii  +  510  pages,  6X9,  178  figures.     Cloth,  $4.00  net. 
(17/-  net) 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


.  v  •  .  . 


REC'D  LD 

JUN2S196Q 


LD  21-100m-9,'47(A5702sl6)476 


323 


3-7 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


